fact: Definition total_set_category_has_pb_ump {C₁ C₂ : setcategory} {F : C₁ ⟶ C₂} {G₁ : C₁ ⟶ cat_of_setcategory} {G₂ : C₂ ⟶ cat_of_setcategory} (α : G₁ ⟹ F ∙ G₂) (Hα : is_nat_z_iso α) : has_pb_ump (@make_pb_cone bicat_of_strict_cats C₁ (total_setcategory_of_set_functor G₂) C₂ F (pr1_total_category_of_set_functor G₂) (total_setcategory_of_set_functor G₁) (pr1_total_category_of_set_functor G₁) (functor_total_category_of_set_functor F α) (make_invertible_2cell (is_invertible_2cell_bicat_of_strict_cat (functor_total_category_of_set_functor_comm F α) (is_nat_z_iso_functor_total_category_of_set_functor_comm F α)))).
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Setcategories UniMath.CategoryTheory.Categories.CategoryOfSetCategories UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.DisplayedCats.StreetOpFibration UniMath.CategoryTheory.GrothendieckConstruction.TotalCategory UniMath.CategoryTheory.GrothendieckConstruction.IsosInTotal UniMath.CategoryTheory.GrothendieckConstruction.IsOpfibration UniMath.CategoryTheory.GrothendieckConstruction.IsPullback UniMath.CategoryTheory.GrothendieckConstruction.Projection UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.Morphisms.InternalStreetOpFibration UniMath.Bicategories.Morphisms.Examples.FibrationsInStrictCats UniMath.Bicategories.Core.Examples.StrictCats UniMath.Bicategories.DisplayedBicats.DispBicat UniMath.Bicategories.DisplayedBicats.DispPseudofunctor UniMath.Bicategories.DisplayedBicats.CleavingOfBicat UniMath.Bicategories.DisplayedBicats.CartesianPseudoFunctor UniMath.Bicategories.DisplayedBicats.Examples.Codomain UniMath.Bicategories.DisplayedBicats.Examples.FunctorsIntoCat UniMath.Bicategories.DisplayedBicats.Examples.DisplayMapBicatToDispBicat UniMath.Bicategories.DisplayedBicats.ExamplesOfCleavings.CodomainCleaving UniMath.Bicategories.DisplayedBicats.ExamplesOfCleavings.FunctorsIntoCatCleaving UniMath.Bicategories.Limits.Products UniMath.Bicategories.Limits.Pullbacks UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat UniMath.Bicategories.PseudoFunctors.PseudoFunctor UniMath.Bicategories.PseudoFunctors.Examples.Identity UniMath.Bicategories.Logic.ComprehensionBicat