Take the tour ×  We can form a braided monoidal category by
taking the groupoid coproduct of the Artin braid groups $B_n$.
We can also make the braids into a simiplical set where the ith
face operation is removing the i-th strand and the ith
degeneracy operation doubling the ith strand. (These operations
are not group homomorphisms, so we don't get a simplicial
group.)  Are these two notions compatible? For example, can we
use the tensor product of the braided monodial category to
describe these face and degeneracy operations? or vice versa? is
there a 2-category or something that can combine these two
notions?  share|improve this question Colin: did you mean 'don't
get a simplicial group' in line 4 –  Tim Porter Sep 25 '10 at
12:57 thanks. i've changed it –  Colin Tan Sep 25 '10 at 13:00
add comment  1 Answer  up vote 9 down vote accepted  I think the
best way to think about this is in terms of operads.  Braided
monoidal categories are representations of an operad $\Pi$ in
the category of (small) categories.