Definition universal_bicat_of_univ_cats : has_bincoprod_ump (make_bincoprod_cocone Z κ₁ κ₂). Proof. split. - intro W. use make_bincoprod_1cell. + exact (pb_of_sum_cats W). + use nat_z_iso_to_invertible_2cell. exact (pb_of_sum_cats_inl W). + use nat_z_iso_to_invertible_2cell. exact (pb_of_sum_cats_inr W). - intros W φ ψ α β. use iscontraprop1. + exact (pb_of_sum_cats_nat_trans_unique α β). + simple refine (_ ,, _ ,, _). * exact (pb_of_sum_cats_nat_trans α β). * exact (pb_of_sum_cats_nat_trans_inl α β). * exact (pb_of_sum_cats_nat_trans_inr α β). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Categories.StandardCategories. Require Import UniMath.CategoryTheory.Categories.EilenbergMoore. Require Import UniMath.CategoryTheory.Categories.KleisliCategory. Require Import UniMath.CategoryTheory.CategorySum. Require Import UniMath.CategoryTheory.IsoCommaCategory. Require Import UniMath.CategoryTheory.Monads.Monads. Require Import UniMath.CategoryTheory.Monads.KleisliCategory. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.CategoryTheory.DisplayedCats.Examples.Reindexing. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.Subcategory.Core. Require Import UniMath.CategoryTheory.Subcategory.Full. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.Examples.MonadsLax. Require Import UniMath.Bicategories.Morphisms.FullyFaithful. Require Import UniMath.Bicategories.Morphisms.Examples.MorphismsInBicatOfUnivCats. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.Core.Examples.OpMorBicat. Require Import UniMath.Bicategories.Colimits.Initial. Require Import UniMath.Bicategories.Colimits.Coproducts. Require Import UniMath.Bicategories.Colimits.Extensive. Require Import UniMath.Bicategories.Colimits.KleisliObjects. Require Import UniMath.Bicategories.Limits.Pullbacks. Require Import UniMath.Bicategories.Limits.PullbackFunctions. Require Import UniMath.Bicategories.Limits.CommaObjects. Require Import UniMath.Bicategories.Limits.Examples.BicatOfUnivCatsLimits. Require Import UniMath.Bicategories.Monads.Examples.MonadsInBicatOfUnivCats. Require Import UniMath.Bicategories.Monads.Examples.MonadsInOp1Bicat.