think to Hawaii. My name is Kim Lau and this show is called Hawaii Rising. The focus of the show is on people helping others to develop the community as well as the economy because that's the only way that we'll be able to create a sustainable future for Hawaii. So some might not believe that investing in market strategies is very important for nonprofit organizations but it actually is quite beneficial for nonprofits to market themselves. Nonprofits can use marketing tactics to assist with growth, funding and prosperity and helping to let people know what their mission actually is because nonprofits need to engage in diverse groups of stakeholders so they have people that fund them as well as clients that they serve and they need to market to both these audiences. They need to show their experiences, their products, their behaviors, their causes and market the organization themselves so their marketing can be very complex. Despite of the lack of a huge resources for marketing campaigns in the nonprofit world there are nonprofit organizations that have some of the highest brand recognition and loyalty and some of these nonprofits you might recognize such as the Red Cross, UNICEF, the Boys and Girls Club and also Girl Scouts of America. So today I'd like to introduce you to an organization who is trying to help local nonprofits to create this marketing and brand recognition here in Hawaii. So we have on our show today Debbie Lee from Adept Hawaii. Welcome to the show Debbie. Thanks. So this is Adept Hawaii is not your actual job right? No so I'm actually working at American Savings Bank as their marketing specialist. I'm just doing Adept Hawaii on the side as a volunteer project kind of thing. So marketing and advertising is your actual profession? Yes so I've been in the industry for about five years so not too long but I'm still I'm still kind of getting my feet wet. I'm actually learning a lot through Adept Hawaii as well. Okay so why do you think Adept Hawaii is beneficial for nonprofits here? Well a lot of nonprofits in Hawaii they don't have the budget for marketing and marketing is actually one of the most important things for an organization especially if you're nonprofits to get the word out so this is kind of our way for marketing professionals to give back to the community. I see so a lot of you out there might be wondering what is Adept Hawaii so let's talk about that next let's talk about what what Adept Hawaii actually is. So Adept Hawaii is a team-based marketing campaign competition so we have marketing and advertising professionals come together to create little mini agency teams and what they do is they create custom marketing campaigns for our selected nonprofits for Adept Hawaii so this year we actually have four nonprofits that have been selected and we're in the process of gathering our professionals to want to come and volunteer. And how long has Adept Hawaii been doing this? This is our third year. And how many so you said there's four nonprofits this year is that kind of the normal trend of how many nonprofits are chosen in the last couple years? It kind of varies from year to year. The first year we had I want to say five last year we had six so we kind of increased it a little but this year we're going back down to four so it's just we're still kind of playing with the numbers. And can you give me some examples of some of the nonprofits that have participated and perhaps won the last couple years? So the first year which is 2014 the winner was Kumukuhua Theater and last year our winners was Hugs so they both received custom marketing campaigns through Adept Hawaii. And if you don't win if you're not the winner can you still take what that marketing campaign that was provided? So actually everybody at the event is a winner whether you're a marketing professional or a nonprofit so all the nonprofits they walk with a free custom marketing campaign and all the marketing professionals you get to network and just meet different different people in the industry so you walk away with new friends and new contacts. I see and this year I understand that Adept Hawaii integrated a new part into this not just marketing. So we do have a new component this year it's called the Tiger Team event so what this we what we've noticed in the past was that although these winner these winners won custom marketing campaigns they weren't really able to implement these marketing campaigns and we found out maybe because they weren't ready the organization wasn't ready for this marketing campaign so what we did was we did this new Tiger Team event and we gather like operations experts HR professionals lawyers attorneys finance professionals and business strategists and they all come together to do a comprehensive assessment on the nonprofits that are interested in participating. And this was already completed for this year's session? Yes so that was held in July Adept usually falls around the fall time every year so it was that was a new part this year so it kind of brought our ad update a little earlier. So again the purpose of the Tiger Team is maybe getting the nonprofits ready for an actual marketing campaign because you can't really market anything if you don't have a product a good product or service ready to go to market. Yeah and even if they're not ready they walk away with knowing what to do for the organization. Oh that's right because we're talking like business strategy maybe like business plans or looking at your finances like your general ledger or things like that which is kind of the foundation for any type of profit or nonprofit organization. Yeah so they got a lot of feedback from these different professionals on what what what is going very well and what they need help on as well. And also like lawyers you said like employee law and things like that and so I think that's good because they probably wouldn't be able to afford this type of like professional services in general right. And it's all free. Yeah that's amazing so maybe next year more nonprofits will think about I guess how did it go this year? This year went very well so we got a lot of feedback from the volunteers as well as the nonprofits. It was interesting for all these different volunteers to come together and work because they don't really work with people from these different industries so it was kind of nice to see them mingle and hear feedback from these different I guess perspectives of the business. Right it's like a lawyer and an HR person or a fundraising person right or an accountant right. So both sides like both the the professionals and the nonprofits found that it was just that exercise in itself was value-added. Yes it was. Nice so I guess that'll be part of the program next year going forward. Yes I think we're gonna start implementing that it'll just it'll it'll streamline the process a little more so the nonprofits will know whether they're ready to participate in add up or if they should you know hold off another year or so. Right yeah so even if they don't like you said even if they don't go forward in the marketing campaign portion of add up it was still value added for them to look at their foundation first. Nice that's kind of cool. Yeah so add up is is a nonprofit sort of thing it's it's not like you're making money off of this. No so we do have sponsors this year Kaiser Permanente is our presenting sponsor and we also have first Hawaiian Bank Pro Service and also the arts at Mark's Garage sponsoring the events this year.  They were. Okay nice so when is the actual add up marketing campaign I guess competition itself. So that is actually on Saturday September 24th it's a full day's worth it's a full day's event so while these marketing professionals are working on these campaigns we also have workshops for nonprofits so these workshops are to kind of educate them more about marketing and how to market your nonprofit. This workshop is ten dollars it includes lunch and some of our past workshops included branding social media and we also had a media panel last year that had people from different I guess media because we had like white news now and some radio reps so. We used to like print TV radio yes like different like media types. Yeah so they're able to ask questions and interact with the media panel to see what stories will catch their attention to get their story on air or on print. So when the day of the actual marketing competition event so then the nonprofits that are in the event will they be working directly with the professional teams. Not so much the professional teams they go off on their own and then we'll have you know our lunch break where they can kind of collaborate again with the nonprofits and kind of touch base make sure they're going in the right direction but other than that the professionals are all on their own and they see the results at the end when they present. Oh so it's a surprise the marketing campaign is a surprise for the nonprofits that are participating but the nonprofits can come during the entire day for these workshops. Yes but not only the nonprofits that are in the event. It's open to everyone. Everyone so not just nonprofits too. Yes so whether you're interested in learning more about marketing on social media or you know anything about that it's open to anybody it's $10. We're still I think we're still finalizing our workshops for this year but it should be good. Okay and tell me again what date is it. It's on Saturday September 24th so it's a full day event. It starts at 8 a.m. and ends at 6 30 p.m. so our winners are announced at 6 30 and then we're gonna have a wrap-up party after that so. And is there a website for people that kind of check out with maybe who's presenting at the workshops or such. So they can check out our website adaphoi.com. All the information should be up there soon. Okay and then they can register for the event off of the link on the website. Yes okay and maybe can you give an example of some of the media professionals or not media but I guess advertising professionals that participate and maybe like people who have done the workshop in the past. Well we have a bunch of people coming to the workshop so I don't know exactly I guess who was representing but we saw lots of representations from different local nonprofits last year and as far as marketing professionals we have people participating who work on like the client side and as well as agency side so we have like MVMP and anthology people there as well to offer their professional help. I see and so again what type of marketing professionals are participating in this sort of event. So we're looking for account service people for creatives like copywriters graphic designers yeah okay that's awesome well that sounds like a really cool event and we're gonna take a quick break right now but when we come back we're gonna talk about how nonprofits as well as professionals can get more involved as they want to participate in this year's event. So this is Kimla with Think Tech Hawaii this show is called Hawaii Rising. Aloha my name is Danelia D-A-N-E-L-I-A and I'm the other half of the duo John Newman welcome. We are co-hosts of a show called Keys to Success which is live on the Think Tech live network series weekly on Thursdays at 11 a.m. we're looking forward to seeing you then. Aloha. Hi I'm Chris Leetham with The Economy and You and I'd like to invite you each week to come watch my show each Wednesday at 3 p.m. Hi I'm Donna Blanchard I'm the host of Center Stage which is on Wednesdays at 2 o'clock here on Think Tech. On Center Stage I talk with artists about not only what they do and how they do it but the meat of the conversation for me is why they do it why we go through this a lot of us are not making our livings doing this and a lot of us would do this with our last dying breath if we had to that choice and that's what I love to talk to people about I hope you enjoy watching it and I hope you get inspired because there's an artist inside you too. Join us on Center Stage at 2 o'clock on Wednesdays. Bye. Hi and welcome back to Think Tech Hawaii. My name is Kim Lau and this show is called Hawaii Rising. Today on the show we have Debbie Lee who's on the planning community for Adup Hawaii and we're just talking about the Adup Hawaii event. So again what's the date for the actual Adup Hawaii marketing campaign competition. So the actual event is on Saturday September 24th at the Box Jelly from 8 a.m. to 6 30 p.m. and we just saw a commercial with featuring Donna Blanchard who was actually the first winner of Adup because she's the executive director of Kumakuhu Theater. So hopefully Donna will be there and she can share her experiences and how it went for her. Yeah so she was our winner of our first year and she's actually part of our Adup committee right now so she's we're getting a lot of input from her what what went well and what we need to improve on and just from the nonprofit standpoint. That's good that you take into consideration like how things went in the past and again that's why you added the Tiger Team event as well. So like we're saying how can first of all nonprofits get involved in this year's Adup Hawaii event. So for this year's event the actual nonprofits we've actually selected our our final four nonprofits. So that is close for this year but we do have the marketing workshops available for the other nonprofits if they're interested. It will also be at Box Jelly and it'll be $10 per person including lunch. They'll learn a lot whether it's like branding social media. Well we're still working up our schedule but we should have that finalized soon. And so that will be from 8 to 8.30 to 6. Is that what you said? Well the workshop start a little later I don't have I think it's around 9 or so they can come early we're gonna have breakfast and the workshop will start after that. So for $10 you get pretty much a whole day's worth of workshop breakfast and lunch. Yeah that's a pretty good deal. That is. And so that's things that everyone could use like social media, branding, marketing, things like that. Like that'd be interesting for me. So I guess what you're saying is that it's not just nonprofits that can attend. It can be general public or even for profit companies can attend as well at workshops itself. And what about if professionals want to get involved in maybe volunteering for ADAP? So we're actually on the search for I guess marketing professionals to help out with Adapuayi. So our first mixer is this Thursday at the arts at Marx Garage at 5.30 p.m. So this mixer is just a networking mixer for all these marketing professionals to come together and just to network and you know mingle. We're gonna have a second mixer that will be September 22nd which is two days before the actual event. And these marketing professionals will be actually trying to create their teams that night. So we're gonna have some fun activities where they can bond with their team and just kind of meet each other and be comfortable with each other before the actual event. Sorry. So how can people sign up for these events? So for the first mixer on Thursday, you can register at adapromixer.eventbrite.com. Okay, that was one more time. adapromixer.eventbrite.com and that will register them for the mixer at arts at Marx. Yes. And is there a charge for that? No, it's completely free. So both mixers are completely free. Yes. And we're gonna have we're gonna start light poo-poo so free food. Yeah. So there'll be free food and then you can buy drinks if you want and and all any all marketing professionals are invited to come for free. Yes. Okay, nice. And so can you give those dates one more time? Sure. So the first mixer is this Thursday, August 25. It'll be from 5.30 to 8 o'clock at the arts at Marx garage. And the second mixer will be on Thursday, September 22 from 5.30 to 8 o'clock at bar 35. Okay, so again, this is not like you have to come and do anything hardcore at these events. Like it's mostly a professional mixer to meet other professionals in the industry. And then kind of feel out if you want to participate in the actual adap competition. So this event is just the like an informational kind of thing where you can learn more about ad up and how you volunteering will help benefit these nonprofits. I see. And so maybe can you describe what the day would be like for people who want to for professionals that want to volunteer for the actual ad up event? Maybe what what would that competition day be like? So they should be arriving around eight o'clock. We do have some stragglers coming in that haven't registered or during the team. So we'll have those people and we'll separate them into groups. And once they come together, we're all going to come together as a group to introduction of ad up and thank you for you know, thank you for volunteering. And we'll also have some word for from our sponsors as well. And then after we get get that situation, we'll have a team captain from each team come up and select a nonprofit out of the hat. Oh, so it's a surprise. Yes. So it's completely random. They don't know who they're going to get so you can't, you know, research the nonprofit the night before or prepare for it in any way. And so once the teams and the nonprofits that the team will be representing is selected, then how would they go forward creating like a campaign? So they'll they'll all be in like a meeting room or some sort of the box jelly. We're going to have the nonprofit join them for the first 15 minutes or so just to kind of brief them on their nonprofits if they have any questions, the team is going to have access to their application which has all the information about the nonprofit, kind of analyze that from there. And then the nonprofits going to join the workshop, which will be held outside in the main area at the box jelly while the team is collaborating on the marketing campaign.  There's a winner, right? Yes. So we are going to have judges. We're still working on our judges, but we're going to have maybe about five or six judges this year, like top execs from top companies in Hawaii. So it's a good networking event where you can meet these these judges and just create more contact. So there is a winner at the end and they get a professional trophy and they have bragging rights to winning the competition. Thanks. But again, like you said, everyone every nonprofit that participates comes away with a marketing campaign that was designed especially for them. So they can take that and choose to go forward with it if they want. That's right. Well, that's pretty cool. And again, all of this is free. Yes. Oh, nice. So if they were to pay for something like this, could you estimate how much these types of professional services are actually worth? Well, of course, it depends on the marketing campaign. But it would, I guess on the low end of the stick, it would be around $30,000. Oh, wow. Yeah, to actually implement an actual marketing campaign. But this they have they're going to do the outline for you pretty much have the backbone for is just implementing the campaign. So can you maybe describe what a campaign would be like? Would it be a print ad or would it be like a commercial or maybe give an example of some of the previous years what people came away with? Well, of course, it depends on the campaign. So it could include commercials, but like how we had this year, the Tiger team event.   So the he actually works with them on a regular basis. Oh, so again, that's another way for maybe not just professionals to network, but for the nonprofits to network with the professionals that they might not ever be in contact with. And then they can come away with, I guess professionals can offer to help them in the future pro bono or they can hire them for professional services. Yeah, so it benefits both sides. Yeah, that's cool. So did those freelancers, do they make like a commercial maybe for Kumo? They haven't, but I think they're, I think they do advertising for a Kumukuhua Theatre. I'm not too sure exactly what they do, but I know Donna works really closely with him and they work on a regular basis. Oh, and I, but for them, the competition itself, what kind of, I guess, marketing, was it an outlying for like a commercial or that they would, they would win? Well, it's, it's an outline for, I guess, the marketing campaign for their entire organization. Oh, so it'd be like branding and like kind of their direction. Or if they have like an event that they're trying to promote, like how to tie this event back to their organization to help sell it to the public. So it's more appealing to attend or, or like, I guess, matches their mission and shows how it furthers their goals and values and such. Oh, I see. Cause that that's really hard for any organization is, is to, you know, brand and advertise and market things like that and cohesively. Yeah. So a lot of nonprofits, they don't, they don't have marketing departments or like, they don't outsource because of their budget. So it's really beneficial for them when they participate in Adapoyee, whether they implemented or not, they know what they walk away knowing what they need to work on and what they're doing great at. Oh, that's true. So even if they don't, like you said, actually implementing, like going out and making a commercial or like buying space for a print ad or something like that is really expensive. It can cost up to like $30,000. But even if they can't afford to go forward with those types of things, they like have a brand in mind or they have like a vision of where, where they should be heading as an organization. Yes. I see it.  So it gives the organization as well as our board members something to work with and what to strive towards. That's true. So, I mean, Adapoy isn't just marketing now, right? It's, it's kind of helping them with their business. Yeah. Their whole organization. And again, all of these services are free. Yes. That's amazing. That's really cool that nonprofits, that people, that professionals in the community actually want to help nonprofits with these types of services. Yeah. And do you find that, um, I guess professionals that participate in these events? They want to maybe do it again or they offer their services pro bono for the teams that they're working with? So we actually have some people returning this year that have participated in the past two years. They just, they said it was a great experience and the event was, it was really worthwhile. So they wanted to, you know, continue giving back to the community. It's only one day. Right. So it's not a big commitment. Yeah. Nice. And, um, are you aware of other, um, I guess when the nonprofits and the professionals meet, are you aware that they, um, they said, oh, if you need help in the future, just give me a call or something like that. We do have some professionals that reach out to the nonprofit that they worked with to see if they, you know, they do need help bringing their marketing campaign further or kind of tips on, you know, what, what else they can do with it. Nice. That's really cool that, um, you can make those connections as well. So, um, again, can you give me the dates for the mix, the two mixers that are coming up and then the actual ADAP, um, competition itself? Sure. So the first mixer is this Thursday, August 25th. It'll be at the Arts at Mark's Garage. That's going to be from five 30 to eight o'clock. Um, you can RSVP for that event at adapromixer.com or adapromixer.eventbrite.com. And then the second mixer will be on September 22nd. That's a Thursday as well. That'll be from five 30 to eight o'clock at bar 35 in downtown. So that one, you can RSVP at adapteammixer.eventbrite.com. And then all of this information is on that ADAP Hawaii website. Yes. Or you can have like us on Facebook. Um, you'll get our updates. We, if you're interested in participating next year, then you can also, you know, get our updates and kind of know what's, what's happening with us. Oh, nice. So if they want to follow you, then just like you on Facebook. Yes. Nice. Well, thank you so much for being here today and sharing, um, the information on the adapue events that are coming up. So any nonprofits or professionals out there that would like to participate in the events, um, just refer to the adapue.com website or like them on Facebook. So my name is Kim Lau and this show has been What You Rising. Thank you again, Debbie Lee for coming. Thanks for having me.


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Okay, hi, my name is Shayna Haralczyk and recently I've been consulting at a lot of small historical societies and house museums It's an interesting environment to work in and we're sort of confronted with a lot of unusual situations Definitely an issue we're always dealing with is trying to stretch the dollar usually our only access to Conservators is when you're conserving a specific piece Which means that for many of the day-to-day issues when you're just trying to store materials say in an attic Or a basement or some other area of the building that you've retrofitted or when you're building mounts You don't have that access base to draw upon so for me It would be extremely helpful to have a listserv or some other form of way to get in contact with Conservators on an informal basis where you can ask those day-to-day questions that may not be concerned about conserving a specific piece and then sort of linked to that a lot of what we Of course in the historical societies is on extremely small budgets so having access to Finding out about materials that may be alternatives That could be purchased a lot more cheaply another issue along the same lines is I'm interested in the possibility of Whether or not there could be a consortium for a purchasing consortium So lots of smaller institutions might be able to pool together the resources and buy things in larger quantities That can then be redistributed to the group


Hey friends tonight, we are hanging out at Universal Studios Orlando, and we are going to be celebrating Mardi Gras This is such a cool event with amazing food from all around the world some really cool Entertainment and an awesome parade, so I figured we come on out eat some food throw some beads and just have a beautiful Universal Studios kind of day any hoos Let's go do this And here we are we have made it Universal Studios, Florida Universal's Mardi Gras International flavors of carnival taking place February 4th till April 16th, and I am so excited I can't wait to try all the food and show you guys around Like I mentioned there is this awesome parade at the end of the night with some really catchy music And there's people tossing beads and you can actually go on the floats Like you can be in the parade and throw the beads to all the guests and it's really cool They have a virtual queue that they released that you could do it or you can do a dining experience where you pay 86.99 I think it is and you get a three course meal and a guaranteed spot to go on the floats So I think we're gonna try to do that today. If not, then we're just gonna watch it a Part of the Mardi Gras festival you can actually get a food and beverage card And you get to actually save some money So if you pay $65 then you get a 75 card $75 card and lanyard and then for annual pass holders if you pay $120 you get a hundred fifty dollar card and a lanyard And I like this I like when festivals like food things well They have like cards like this so you can go around because I think it's more convenient Universal has actually invited me out so that I can give you guys a better look at some of this year's Offerings and we're gonna do a little special event and then we're gonna head on out go to our dinner get ready for the float and try some food Something else that's really cool about this event You don't even need to go into the park itself because they have tons of activities out on city walk And all you have to do is just come in like paid a park and they have the cursed coconut club That is really cool It's kind of a Mardi Gras or voodoo themed a bar and then they've got patty O'Brien's some food stands like that We're inside the park are actually out on city walk So you can actually just come and enjoy without actually buying a park ticket This year's Mardi Gras has food from over 17 countries around the world and because we're doing a little special event They're gonna give us some of the items so that we can try now But once we go in the park I plan on showing you around to some of the different booths and then don't forget I think we're gonna try to still get dinner so that we can ride the float Looks like they've got some fresh Benye's for us to try might as well get myself a bag of Benye's and then they have Babor cata cata and it's kind of like a rice pudding like a sticky sticky sticky rice I don't think I've ever had anything like this. I think it's Indian So I'm gonna try it. This is kind of adventurous for me because I'm eating something I literally have no idea what it is actually. I know it's some type of rice, so we're going for it I don't know. It kind of looks like blueberry filling though. Oh That's delicious. It tastes like rice pudding I actually do enjoy this a lot. I Also decided at trying some of the Mufongo and this looks really good. It's got a little shrimp in there I don't think I've ever had that before and here's just a quick peek at the Benye's in the bag The Benye's in the bag. I like when they do this because then you can shake it up and make sure they got extra sugar on them Might as well try more new things and since I tried that little rice pudding dish I think I'm gonna do the most Little more fun. I've never had this before so I have no idea what the taste or the texture is I'm just gonna try it. I'm gonna give it a go Okay It's very good reminds me of stuffing actually This is actually really really good. I do like it, but now It's time for the Benye's. It's time to get down to the Benye business These Benye's are so light and fluffy and you know Benye's go good with Mardi Gras along with Hurricanes and Jambalaya and gumbo which I can't wait to try some Jambalaya and gumbo because you know that it's Definitely a must but nice little Benye's a good way to start. So here we go. Cheers. Oh Yeah That's a good Benye It's definitely a Benye and not a Ben. No, but look at that So delicious. That's the way now I've never had Benye's from like say New Orleans before so I don't know if they should be Airy or should they be thick and you know kind of like fluffy all I can like describe Benye's is how I've had them either here in Universal or Disney or oh Disney land. So I don't know which one is kind of more traditional, you know Look at me being fancy trying new things Trying new things once I thought I was done Something brought me back for more and that is the liege waffle with strawberries and cream. Look at this I literally was just like, you know what? I'm done, but I can't pass up a liege waffle. It looks too good. I Love how these waffles are kind of doing like a big like if they're the kind of like very trendy right now You get the liege waffle over an f-cott. I see them all over the place In fact, there is a restaurant near my house that just sells Leage waffles like they sell waffles and like chicken and stuff like that. So I'm excited to try this one because it looks pretty good It looks a little flaky actually you can actually pick this up and have like a waffle taco. Oh wait a second that does exist I feel Seriously just look at this. All right. Here we go That got on my nose, but it is amazing look at my nose The sugar crystals are amazing. This is much too good honestly so good Well, that was a lot of fun I'm glad I got to try a little bit of the sampling of the different items in the food booths Now we're gonna actually make our way over to Lombards because that's where we actually got our dining reservation For our dine-in float ride But we do want to try some more of the items like I said Maybe some jambalaya some gumbo and it's all smaller portions So you get to actually enjoy and try different things without actually getting full but the Lombards that's a three-course meal Like I mentioned they have some of the food booths actually right out on city walk and this year They're even having some over at islands of adventure and 17 different countries Look at the taste of the Mediterranean So they have like a grilled octopus with rice and then a crepe Cezette, I've never even heard of this, but it comes with Grand Marnay orange sauce which sounds amazing And then over on this side. I think they actually have like a New Orleans style food right next to Fat Tuesday Kind of appropriately right here I wanted to wear something a little bit Mardi Gras-ish and I didn't know what to wear and since I've come to Universal Studios I decided to wear my Tiki tunes Nickelodeon Roosevelt and look at this shirt. It's like a 90s nostalgic all wrapped up in one Look at all the characters on there. I love this shirt so much Now that we have made it into the park You can actually see a lot of the entertainment just hanging around the characters And this is cool because you get to see it during the parade and then actually just throughout the whole entire day I love it. It's so festive. Oh, and they even got some beads Very nice my friend The parade has several themed different floats Of course, they always have like their returning favorites like the river boats and the king and queen float But they always have new ones and on opening night I actually was here and I was throwing beads, but I wasn't making videos and I was on serpent So I'm excited to see what float we actually get this time and the performance that you'll see walking around Some of them are all separately themed to different things too One of the things I have to say about Universal Studios is their entertainment is honestly next level It's also important to point out that everybody celebrates the Mardi Gras season even Scooby and Shaggy look at that That is kind of cool The Mardi Gras float in Dine experience is actually 84.99 per person and you can choose between Finnegan's Lumbar's NBC or cowfish, which are all amazing restaurants Lumbar's is the one that popped up now They all have separate availability yet to pick the restaurant first and you could do this in the Universal app and Once you do that They give you like a little lay in your and you're able to go and actually have a reserved spot for the floats themselves And it's hard to get on those floats like those virtual cues go like that Little street performance too Seriously, there is just non-stop entertainment throughout the whole entire day And it only gets better as night time closes in I love it so much And here we go We have made it to our restaurant Lumbar's seafood grill And they even have a special Mardi Gras dish on the menu and you know, we're definitely gonna have to get that Now that we have checked in they gave us our little lanyards We had a prepay for this so we just sit down order what we want And then we can leave and I also found out that we get our annual past discount It was 84.99 on the app, but when we booked it, I think it was a little cheaper So our AP our like our AP discount ended up being around 55 dollars per person and that's amazing I mean, that's that's a that's a deal and a half Lumbar's is such a pretty restaurant every time I come in here I say it like I feel so elegant eating here We got fish fountains and the lobby Nice carpet the chairs are fancy It's very nice Look at big fish tank right in the center of the room Now that we have made it to Lumbar's I want to go over the menu with you try to figure out what we're going to eat and Have a little fun Here is a look at the menu and because we're doing the dining package It's all three courses. So we get one appetizer one entrée and then one dessert and they've got some nice things for appetizers I've got street shrimp cocktail calamari tuna poke and then for entrees because it's Lumbar's it's a lot of fish So like they have the fishermen's basket fishing chips They've got uh, brand zeno But what i'm interested in is this bayou shrimp and it has the little mardi gras sign next to it So that's like a special or a favorite that they're doing just for the mardi gras season And it looks good and then dessert. I don't know what to look and see but I think i'm going uh I think i'm going calamari and bayou shrimp a little bayou shrimp I have eaten here before in the past and the food is always amazing It's so good, especially if you love fish and i'm excited to dive into the uh Calamari that I got but more excited for probably the bayou shrimp down by the bayou Here is the calamari and at first I got nervous because I was like what's that red sauce under there I hope it's not like something I wouldn't like but it's the good old marinara And that's what I like some nice little calamari the italian way Joining me on the parade float tonight is a really fun crew Look at you guys already and I like the shirts. Look at these are actually fitting very very fitting like Oh, yeah, there is yeah, there's a lot of them So I hope we get that one that would be cool And then we also have ashlyn and promise and chris the gang's all here everyone's having fun Yeah, we party large Here we go it's time to try the calamari it's very crispy I can already tell lots and lots of good texture here Oh, that is good Chris, what did you order? What did you order?  All right, this is the Cadillac old-fashioned. Oh the Cadillac. Yes apple pie old-fashioned Yes, this is the classic old-fashioned.  Holy moly We're like all like we don't know what to say And just like that dinner has arrived I ended up getting the shrimp bayou or the bayou shrimp The only thing is is I don't see any of the sausage on here. Did you see any sausage or is it in it? It's in the cake. Wow Yeah, there's like a little fried grits cake there the shrimp looked good And then the sauce is good and then I think we have some cream spinach under there So we're going to dive right on in. I only wish they had more than four shrimp You know what I mean? I feel like shrimp should only come out like six and 12 six and 12 Six and 12 A half dozen a baker's dozen I'm going to try the shrimp on its own first and then we're going to try it with the grip cake I do like a little grip cake. I don't think I've ever had it before but now that I know sausage is on the inside Cut that's my kind of cake Wow The power of that shrimp That's good Now I'm going to try a little bit of this grip cake here. Oh, it's got a little spice to it It's creeping in on me creeping in. Look at that Honestly, it looks like a crab cake Crab tree. There we go. Let's grab a little bit of this a little bit of that Seriously look at that It looks so good. I really do like this a lot I feel like I need to get more. I just wish I had a little bit more shrimp. That's all I'm looking for Everybody else had some good food though. It's all gone. It's all gone. I'm the slow eater. Where'd it go? Was it that good? What'd you have? Swordfish I missed the song. I'm gonna have to watch your video now. I'm I missed it all Enough of the bayou shrimp business. It's time for desserts. Look at all these desserts They got a chocolate cake a key lime pie a mocha triangle. I went with the key lime pie though Look at that. Oh, yeah, that could be a dessert Here we go a little key lime pie time Key lime pie time. I like that got the end piece I like it I'll trade you some of my key lime pie for some of your mocha triangle That's a deal. That sounds like a good trade. That's a good deal. We're gonna scuba do a little scuba do scuba do There we go That's the way cheers That was amazing such a great value honestly Because like I said if they just sold an individual lighting lane so that we can go and do the bee tossing I probably wouldn't just pay for it. You know what I mean and to have it all together the food was great But I didn't notice that because today is like not a weekend The parade starts earlier than I thought and we have to go check in at 455 before five o'clock So we're gonna head over there and check in so that we can get ourselves our nice little gowns find out what float We're on and then I don't know. Hopefully we can try some more food once we're done If not, I'm gonna be tossing a lot of beads As we're making our way over to the check-in area, you can see we've got some of the stands here Good old belgium and then germany over there I love that they have multiple stands and they have all good drinks and food items This might be one of the best food festivals in Orlando itself Hi, I'm looking at those lige waffles. Those are the stuff right there right there. That's them right there They're so good Amazing, yep Here we go, we have made it over to the check-in area We have our credentials And also if you ever do want to ride the floats, they do do a last-minute drop sometimes So you can always try again with the virtual queue Now we have to get our sashes. I'm so excited to be gator like we're team gator and that's the last Float it's one of the biggest floats too. So it's gonna be our job to bring it home Like we gotta we gotta go hard. We gotta go. We're bringing it. We're going all the way Gator right here team gator I love it. There's a good color on it. I know I like it. I like it. That's so cool and they have all the different Costumes for the different floats.  They're gonna bring you over to where you have to go Team gator The next time you see us, we're gonna be on the float. So here we go Yeah, so many beads So many beads under hand or to the side full experience.  I mean it really doesn't matter at this point Look at the ground I'm like Scoop some of that yet cleanup crew coming in Yeah So many people I was tossing beads to and it was awesome Everyone that was calling out my name and recognized me. I really love that and it was cool Also seeing a lot of friends like Jackie was out there And there was a big group of people in like a separate viewing area that I got to say hi to And then also a little friend made me a little star Beady thing. She made this isn't that nifty? I love it Show me this magic trick You are the magic Now it's time to clean up all of the confetti And that's how the confetti gets vacuumed up Since the park closed at seven o'clock I figured we'd come out to city walk and explore some of the Mardi Gras festivities that they have going on out here They have the new Orleans stand and they have the yaku-men. It's kind of like a ramyun And I kind of looks good. I'm excited to do try this. Look at this braised beef poached shrimp and seven-minute egg over noodles with spicy beef broth yaku-men They also have an old baby beer and it's made by crooked can a local brewery here in winter garden And it tastes like king cake. So it's like a king cake beer. And I I don't think I can pass it up King cake beer you remember that one time you brought a gigantic king cake to uh, uh, port Orleans Yeah I don't know who got it. I remember I just remember Maria bringing a gigantic king cake in Yeah, what cheers oh, baby. Oh, baby I'm excited to give this a go Oh, yeah Here is the yaku-men and it looks so good get a couple shrimps in there I got the egg. I wonder if it's super spicy. I can see the beef in there too. It's a good portion pretty big old cup They actually give you a chopstick fork. Look at this promise to me to open it. Yeah, she said that's a real dingle hopper It's a real dingle hopper. I could look at that chopsticks right in my hair. You don't even have to work to you Yeah, you pinch it or you fork it. That's intervention You fork it All right, I'm going to use my special What did you call them? Chorks Try to find myself some noodles. Oh It doesn't work effectively I'm gonna say it doesn't work effectively I can get one noodle and one piece of beef There we go. That works It's good. I don't like the noodles. I like the beef. The beef is good Not so much the sauce. I'm not not so much the noodles out Yeah, it's very slippery Very very hard to pin down there, but the beef is good. Look at the noodles. They just keep flopping off I tried using the tongs or the the chopstick side the tongs Yeah It is tongs Enough of the yacum in business. I think that's how you say it We're gonna move along and I think we're actually gonna head up to paddle bryans again That's where we started off our day. Maybe that's where we're gonna end it We were gonna make our way back on over to paddle bryans But it looks like they closed it off for a private event a company rented out all of city walk Wow, that's a good company right there Right, what a party.  I figured the only thing that's open actually over here is antohitos And uh, yeah, I mean we're celebrating mardi gras, but we could get a margarita This place is actually a really good restaurant They've got some nice guac and chips and I think we're just gonna grab a little uh a little margarita Mardi gras margarita. I don't even know if that doesn't even sound right. Mardi gras margarita It's probably super loud in here, but I got the watermelon margarita. You guys want to cheers real quick Chris got a watermelon margarita too Cheers Big ol margaritas And with that we ended the night with a little watermelon margarita, which was fantastic I mean the watermelon margarita was way better than I thought it would be but we had a great day Mardi gras was fantastic throwing the beads I wish we could have tried a little bit more of the food inside there But the park closed at seven o'clock and that was like so early because the last time I came I think it was open till nine o'clock And uh, yeah, it's been a fun amazing time Thank you Universal Studios for inviting me out and being able to show you guys all the cool snacks and the beads and everything like that And I hope you enjoyed the video because I enjoyed making it. We'll see you next time Bye And a good Mardi gras tradition. We got to sacrifice our beads to the tree I'm doing them all at once


Hello and thanks for watching this video on bifibration of polycategories and the relation to classical denology. I'm Nicolas Blanco and this is joint work with Noam Zalbego. You can find the draft paper for this talk on my website at VSUile and I will also post the slide on my website. So before going into the details of polycategories, let's first recall some context and especially models of multiplicative linear logic. So to model interesting multiplicative linear logic we can use monidel closed category and for classical multiplicative linear logic we can use start and most category that were introduced by bar or linearly distributive category introduced by croquet and city where a linearly distributive category with joules is equivalent to start and most category and in both case the idea is that you will ask for two models structure a new category that will interpret the tensor and the power and a monoidal duality between those that will interpret the negation. Another way of interpreting logic in you know categorical setting is by using multi-categories. So multi-categories have been introduced by Lambeck so it's some knowledge by Lambeck to represent second calculus to interpret the synestically second calculus. So in a multi-category instead of having morphism that have one input and one input you have multi-maps whereas the domain can have many objects. So using this multi-categories to represent second calculus is inspired on one way on one hand so by the notion of multi-linear map in linear algebra and on the other hand by the interesting second calculus. And so using this interpretation we can define the connective by universal property instead of defining them by structure. This can be extended to classical second calculus by considering polycategories. This has been done and introduced by Zabo which was one of Lambeck's students and the idea is that in a polycategory you have polymap where now you have when up both the domain and co-domain have multiple objects and the cut the sorry the composition is done is done along one object to mimic the cut rule from second calculus. So this makes it different from poor or poor for example where you can compose along multiple objects at the same time. So polycategories have been used by Coquette and Silly to model a multiplicative linear logic in what they called two terms of polycategories with duals and we can also find in the literature the terminology representable star polycategory which is the one that we will use in this talk. And finally I want to mention another line of work by Cloggio Amida. So in the at the beginning of the millennium Amida observed that there are a lot of analogies between multi-category theory on one hand and five-part category theory. So if you go to his nice paper there you will see a table table that recap all these analogies and to make these rigors you introduce the notion of multi-categorical vibration. It's more precisely of co-variant vibration of multi-categories. I did that in 2004 and something that is quite interesting is that multi-categories that are fibered over one over the terminal multi-category are in correspondence with monoidal categories. So this makes this relation precise between representable multi-category on one hand and multi-category fibered over one on the other hand. He also used this theory of vibration of multi-categories to study the algebra for an upgrade. He proved that an algebra for an upgrade is the same thing as a discrete vibration over this operator considered the one object multi-category. After that people have been interested in introduce contra-variant vibration and then bifibration of multi-categories. So it has been used for example recently by Likata Shulman and Wadi to represent some logical structure. This is closely related to the notion of vibration of close categories. So if you take a multi-category that is bifibered over one then it is the same thing as a monoidal close category. If your multi-category is co-variantly fibered over one you get just a monoidal category and to get closeness you need to also ask for it to be contra-variantly fibered over one. And there is an important asymmetry event that is that the pullback so for contra-variant bifibration has to be parametrized by a choice of inputs. For the push forward you don't have to do that because you just have one object in the co-domain but in the domain you have possibly multiple objects so you have to choose one along which will perform this pullback. So in our paper we have several contributions. The first is to define a notion of universal polymap that will be parametrized either by an input or by an output. And using this notion of universal polymap we can get all the connective of mll by saying that they are characterized by the existence of certain universal polymap. So with this analogy in mind we introduce star-representable polycategory which will be polycategory that has all possible universal polymap. And then we prove the following theorem which is our first contribution that this notion of star-representable polycategory is equivalent to the notion of representable star-polycategory that has been studied by Coquette, Silly and others to represent multiplicative linear logic. After that we define the notion of vibration of polycategory that extends the notion of vibration of polycategory. So like in the contra-variant case for polycategories, in the vibration of polycategories the notion of Cartesian polymap will be parametrized by a specific input or specific output. And we prove that the polycategory is bifibred over one if and only if it's star-representable. And so this gives another a correspondence between star-polycategory and polycategory bifibred over one. And so one of first motivation to study that was to study the structure of the star-polycategory and the category of finite-dimensional banana spaces and the contractive map. So something that is really interesting about this this category is that it's a category that comes from the category f of vector spaces. So it has a forgetful function in it. And it is also star-autonomous but it's not compact close contrary to the category of finite-dimensional vector spaces. So there are two norms that you can put that you will put on your tensor project that will give you the tensor and the par all-code projective and injective cross-norm. And they are known in the community of functional analysis. For example, because they have this universal property that they are extremal on the set of norm that you can put on the tensor project. So if you look at any norm that you can put on the tensor project and that is well-behaved in some sense, will lies between those two norms. And we will see that this property of being extremal come from the fact that they are defined using Cartesian polymaps. And finally there is a third contribution that we won't have time to get into the details in this paper, in this talk, sorry, that is polycategorical growth and the correspondences. So we give a collection of different growth and the correspondences in the polycategorical case where, for example, we give correspondences, one-to-one correspondences between one-on-one and bi-fibration of polycategories and on the other hand, pseudo-functors that goes into the two polycategories of multivariable adjunctions. So using this fact, we recover an observation by Max Schumann, but start on this category of Frobenus pulmonary in this two polycategories. So now let's get into it and first define polycategories. So our polycategories will be taken to be planar, which means that they are not necessarily symmetric, basically because it's possible to define that and symmetry doesn't doesn't really play any picture in this story. So you could take symmetric polycategories and do everything that we are doing here with only slightly, slight modification. So we thought it was better to do the more general case. This is in line with the work by Croquet and Cilly, where they consider linearly distributed category to be non-necessarily symmetric. So in particular, the notion of start-on-mouse category that we have is also non-symmetric. So it's planar start-on-mouse category. And in particular for jewels, we have both right and left jewels. That being said, a polycategory is a structure analogous to a category. It has a collection of objects, except that it has a set of polymap from any finite list of objects to any finite list of objects. So the domain and the finite list of objects. These lists can be anti. It should have identities, the notion of composition that are unital associative, that have an intention flow, but will you explain later? So the fact that our polycategories are planar and not necessarily symmetric puts some restriction on the composition, but I will explain just now. By looking at how to represent polymaps graphically. So the idea is that we will represent will represent our string diagrams that goes from left to right. And a polymap will be represented by a box that takes some inputs. So they're gamma and spit out some outputs. So delta so delta one, delta two, and A. Then we will represent composition by plugging the wire from one output of F into one input of G. So we can see that that composition happens only along one wire, one object. And so the planarity condition, which is also known as the no-crossing condition, state that wires should not cross. And so in particular it will, so what it will exactly mean is that either this list or this list is empty, and either this list or this list is empty. Finally, the intention flow say that taking polymap H, and if I want to composite with two polymaps F and G along two different inputs of H, then it shouldn't matter in which order I'm doing it. So I can start by plugging F and then G or the other one. And of course, there is something similar for outputs. Finally, I want to give you some examples that will be important in this talk. First, there is a terminal polycategory. It has only one object and one polymap for each arity. So given two arities M and N, there is a polymap that goes from M copy of star into N copy of star. So this terminal polycategory is trivial. It's not really hard to define, but it will be really important to know the theory. Then given a linear redistributive category, as introduced by Croquet and Silly, or if you would prefer a star autonomous category, which is a special case of linear redistributive category, you can define a polycategory where the polymap goes from the tensor product of the input into the part of the outputs. And in particular, any monodal category can be considered as a linear redistributive category where tensor product and part are taken to be both to coincide. And for star autonomous category, it will give the notion of compact close category. And in this case, of course, we get a polycategory where the polymap are given by the map that goes from the tensor product of the input into the tensor product of the output. So just for information, I'm just recalling the second calculus rules for multiplicatively analogic. If you are not really familiar with it, I invite you to pause the video. And using that, we'll define in a polycategory, which is a tensor object. So a tensor object will be taken to be an object that comes with a binary map that goes from A B into A tensor B. So you can think of vector spaces here. And so it's a billionaire map that goes from two vector spaces into that tensor product. So it should have a universal property that say that any map that has A B in the input should factor uniquely through this A, through this M, this billionaire map. So this is the property in vector space that tensor projects linearize billionaire maps. And we choose this notation because this is closely related to other rules from the second calculus. So this corresponds to the tensor left rule. So given something that has A and B in the input, I get something that has A tensor B in the input. And this M is closely related to the right rule for the tensor product. We get it by looking at the right rule and taking the special case where you have identities. And so by an identity from A, A and B, I should get this map that goes into A tensor B. And this will induce a natural isomorphism that goes between A B and between maps that goes from A B and map polymer that goes from A tensor B. So in one direction, we get this isomorphism by composing with M and on the other direction by factorizing. So this natural isomorphism is represented by this correspondence between these two maps. We have something similar for the power, but where we exchange the notion of input and output. So we'd get a co-binary map, a map that goes out of the power into A B, but as a factorization property where this binary map is now post-composed. So everything factors through the post-composition by W. And natural isomorphism where now we have A Bs in the output and A that gave A power B in the output. Finally, we can define the star in a way that is really similar to the way that it's defined in compact class category by saying that we want two maps that we'll call the cup and the cup, but as this, this typing. So the cup goes from the anti-list into A A star and the cup goes from A star A into the anti-list. So that they satisfied what is called the snake identity. So it's going to say snake identity because if you draw it, so you will get a snake like that. And taking the snake identities is yanking the snake. And so taking the snake and making it an identity. So we'll have both snake identities and this will induce a natural isomorphism between a map with A in the input and map with A star in the output. So using all of this notion, we get the notion of representable star polycategory that has been defined by your eco-cat and series by saying that it is a polycategory that has all times A power left and right joules. So now that we introduce that, we want to give a slightly different definition that use the notion of universality. So the idea is to get one notion or two notion of universal and universal that encompass all of the properties of the connective. So we'll say that the map is universal in one of its inputs or one of its outputs if it has this kind of factorization property. So for example, U is universal if in this output, if any H that has the right kind of typing but will make it a potential composition with you will be indeed a composite. So there will be a unique way to factor H through H, there for you sorry, and very very run for inputs. So it's a same kind of factorization property but now both composing by the universal map. So in particular for there if we take U to be the binary map that goes from the answer from the from A and B into the answer project, then this would be exactly the property of the universal property of the answer project. It will say if I have A, B in the input of a map, then I can factor it to get a map that has A times B in the input. Using that we say that a poly category is star representable. If it has all universal object, what we mean by that is that if you give me some object, some list of objects, that will specify all the input and output of a map except from one. So we will leave one input empty. Then I can give you this input and a poly map that is universal in A and of course the same for outputs. So if everything is specified for the poly map except from one output, I can find this output in a universal way. So such that it comes with a universal map. And if a poly category is star representable, we prove that it is equivalent to the poly category being representable star poly category. So it's equivalent to to be star representable and to have all the answer parts under yours. To do that one way is mostly by definition. So we get by definition that the answer and the power are universal objects. So we get them from star representability. What is maybe a little more surprising is that we can also get duals by the same kind of the same scheme of universal property. So we get for example that the dual, the right dual can be defined as a universal object with respect to a cup map. And the universal property of this cup map will let us define what is a cup and it will have built in the fact that it is a snake and entity. But we could choose the other way around and say, okay, we will define duals by the universal property of the cup. And using this universal property, we can derive a cup that will have the snake equation. Also, we should note that cup and cup are also universal in A. And we can use this fact, for example, to prove that the B dual is equivalent to the object that we started with. And the other way, if you give me representable star poly category, so something that has all the answer parts from duals, I can build star, I can prove that it is a star representable category. So I can build any universal poly map. And how does this work? This work by, so if you give me the typing of the map, except for one object, I want to derive this object and our universal map poly map in this. So the way that we do that is that we use a cup to take all the outputs and put them into inputs by starving them. And then we take all the inputs and we transfer them to get a final object. And so this object will come with this universal poly map. We can do something similar for universal by flipping. So exchanging input and outputs and replacing all the transfer by parts. So the cup will be flipped and we just give cap instead. So this gives us a first contribution, which was to give an alternative definition of what it means for poly categories to be representable. And now we can go and define bifibration of poly categories. So first some terminology will say that we will call the front of poly category, the poly refinement system. This terminology is inspired by the study of the type refinement system as a factor of category. So we will draw them graphically in this way, vertically, where the diagram on the top will be in the domain and the diagram on the bottom will be in the pre domain. And in such a way that things that lie over another one are sent to it by the poly refinement system. So for example, r is sent into a, phi is sent into f. And so this precise diagram is expressing the preservation of composition because it says that a composite is sent into a composite. With this graphical representation, we can give a concise definition of Cartesian poly map. So both in and out Cartesian poly map, which correspond to, for the unit correspond to Cartesian map and the out correspond to Cartesian map. So they are defined for example for out Cartesian in this way by saying that phi is out Cartesian in this output. So it's still parameterized by one, one specific output. If any map that lies over a composition by the image of f will factor for f. So if it's lie over a composition, then it's a composition, basically. And the same is true for in Cartesian with respect to one specific input. So if something lies over a composition by the image of this input, so along the image of this input, then it will be a composition along this input. So something that is interesting here and that I will come back to later, but I want to explain it graphically. It's to give you some sense of white work is that if I take the base category, the base category to be terminal, the terminal category, then all this condition will be trivial. So everything will be trivialized on the base and we can just forget about the base. And we see that this factorization property then becomes just the factorization property of universal map. So this explains why your polycategory that is bifibre over one is the same thing as the star-representable polycategory, because then Cartesianness corresponds to universality. And in the similar vein, if the bottom diagram is a universal diagram, then the top diagram will be universal. And so we can think of Cartesian morphism to be a way to lift universality. So universal map from the bottom polycategory into the top polycategory. Talking of lifting, we called Cartesian lifting any map obtained like that. So given a polymap in the base and if I have the typing of every, so if I have a refinement, if I have an object over every object of the domain and codomain of f, except for one, I should be able to find one object over a in such a way that it comes with a Cartesian polymap that lies over f. And so this object that lies over a, we called the pullback of sigma along f in context pi1 and pi2. We often just refer to it as a pullback. And the map will be called the Cartesian lifting of f. There is something, of course, similar for output. And we called the dual notion of a pullback a push forward. We will also talk about Cartesian lifting. And so finally, a poly refinement system is called a pullfibration or just a fibration. If it has all in Cartesian lifting, it will be called a pushfibration or upfibration. If it has all out Cartesian lifting and a bifibration if both are true. So if it has all Cartesian lifting. And as I said before, a category, a polycategory that is bifibred over one corresponds to star-representable polycategory. And this is just because the notion of Cartesian map will be parametrized by some base polymap that is trivial. And so this will correspond to universal map. And as a corollary, we get that star-autonomous are just represented by polycategories fibred over the terminal polycategory. We can use this to lift the star-autonomous structure. So as I said, if you take the Cartesian lifting of a universal polymap, you get a universal polymap. So Cartesian is a way to lift universal polymap. And so using this fact, if I have a poly refinement system between a base category that is star-representable, so it will have all universal map. And in such a way that this poly refinement system has all Cartesian lifting of universal polymap, then the top category will be star-representable. So this is a way to lift star-autonomous structure, because we will lift all the connectives by just taking the Cartesian lifting. So we can use that as an example that I mentioned before of banana spaces. So first we can define the polycategory of finite-dimensional vector spaces by just using the fact that the category of finite-dimensional vector spaces is compact close. So we get poly-linear maps as a polycategory that are defined by a map that goes from the tensor into the tensor. And then we can define a polycategory of finite-dimensional banana spaces and contractive poly-linear map just by defining what it means to be contractive for a poly-linear map. And so this equation holds that for any object A1 through AM in A1 through AM, and any linear form phi 1 through phi m that goes from any B's into the field, into a by-field, if you want to think of it, object of the duals of the B's. Then when I plug the input into F and I take, so this will give me an output that is in the tensor product of the B's, then I can take this output and give it to the tensor product of all the linear form. This will give me a scalar. And if this scalar is lesser or equal or has an absolute value that is less or equal to the product of the norms of the A's and phi's, then we'll call it contractive. And so in particular if you take F to be a linear map, then this notion will be contractive. So it will be the fact that F is of norm less than 1. So something to notice and that is really important is that we can define this polycategory without mentioning any notion of tensor product in a banana spaces. So we have a tensor product in vector spaces but we don't know how to lift it into banana spaces. And the notion of contractive poly-linear map is, I think, something that is easy to define, especially if you compare it to the notion of tensor product in banana spaces. So from that we get a forgetful function but just forget about the norm. And this forgetful function won't be a bifibration in general but it will have all Cartesian lifting of universal polymap. And we saw that it is enough to lift the star-representable structure. So this will give us a star-representable structure on f-band 1. And we will get, for example, that the tensor product in f-band 1 will be the push forward along the binary map in f-vect, the map that goes from a b to a tensor b. So we take the push forward and this will give us the tensor product. And in the other way around the power will be defined as a pullback along the co-binary map that goes from a tensor b into a b. And if you look, so it's explained in more detail in the paper, that if you look at what are pullbacks and push forward in this category for relatively to this factor when they exist, this gives you that the tensor product is a projective cross-norm and the power is the injective cross-norm. So as I said, I find it really exciting because it's hard to see when you look at this norm that there are indeed the right norm for the tensor and the power, that this thing put a start-almost structure on f-band. But they have this universal property. They have this property of being extremal among all the good norm that you can put on the tensor project. And this reflects exactly the fact that they are defined by a push forward and a pullback. And so this gave us a way to find the start-almost structure on finite dimensional banner spaces by a universal property and just by defining the notion of contractive pullback. Okay, and so to conclude, in this talk I presented to you a vibrational perspective on models of classical multiplicative linear logic by showing to you that start-almost category correspond to poly categories that are bifibred of the one. And using this perspective, I showed you how to lift the start-almost structure along a factor if you have a good notion of poly map on your top category and your factor has enough vibrational property, has enough Cartesian poly map. Something that we also discussed in the paper and that I don't have enough time to go into is a bunch of polycategorical growth and the correspondences. And so in particular, a growth and the correspondence between bifibration of polycategories and pseudo-functor into the two polycategories of multivariable adjunction. And using that, so if you specialize this fact to the base polycategory, being the terminal polycategory, so we know that bifibration over the terminal polycategory are the same thing as start-almost category using the growth and the correspondence. So we can get a pseudo-functor. So this will be equivalent to a pseudo-functor that goes from the terminal polycategory into the two polycategories of multivariable adjunction, which is the same thing. So pseudo-functor out of the terminal polycategory is the same thing as a Frobenus pseudomonade. And so we get that start-almost category and Frobenus pseudomonade are in correspondence. This is something that has been proved and observed by Schullmann recently. So some future work that we'll be interested in is first finding a very interesting example of polycategories of bifibration. Then using polycategories of bifibration to build a polarized model for linear logic. And finally, we will be interested in looking more precisely, specifically, as the case where the base polycategory is compact close, which is, for example, true for vector spaces. And so thanks for listening to this talk. If you have any question, you can contact us on the Slack channel during the conference and feel free to go on my website and check the paper and also check this slide if you want to. I will leave you with this nice table that recap all the models of classical multiplicative linear logic that we talked about in this talk. So first start-almost category where connectives are represented by monodestructure, then representable polycategory where they are represented by universal objects, bifibrate polycategory over one, where they are represented by push forward and pull backs. And finally, for monoid in the two polycategories of multivariable adjunctions, where you get the connective by multiplication and commutification. Thank you.


So to use the distribution factors to calculate power flows, the thing that we realize is that the distribution factors simply tell us the proportion of power that's going to flow on each of these two lines. And so the total amount that's going to flow on each of these two lines is the amount that's produced at the generator times the distribution factor on each of the two lines. So the flow on line one is going to be equal to the amount of power produced at the generator times the distribution factor on line one, which we remember is 1 over 1 plus 1 over alpha. So in this equation, remember that W is the power produced at the generator. And this term right here is just the distribution factor for line one. So the flow on line two is going to be the amount of power that's produced at the generator times the distribution factor on line two, which remember was 1 over alpha divided by 1 plus 1 over alpha. As an example, let's take W is equal to 100 megawatts and we're going to take alpha is going to be equal to 2. So the flow on line one is going to be equal to W times 1 over 1 plus 1 half. So this is going to be equal to 100 times, remember our distribution factor here in this case was going to be 2 thirds. So what we're going to get is 66 and 2 thirds megawatts flowing on line one. So for the flow on line two, that's going to be equal to W or 100 times the distribution factor for line two, which is going to be a half divided by 1 plus 1 half. So this is going to be equal to 100 times 1 third, which is 33 and 1 third megawatts.