Definition bicat_of_cats_has_kleisli_cocone : kleisli_cocone m. Proof. use make_kleisli_cocone. - exact (Kleisli_cat_monad M). - exact (Left_Kleisli_functor M). - exact (kleisli_monad_nat_trans M). - abstract (use nat_trans_eq ; [ apply homset_property | ] ; cbn ; intro x ; exact (η_η_bind M x)). - abstract (use nat_trans_eq ; [ apply homset_property | ] ; cbn ; intro x ; exact (η_bind_bind M x)). 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.Monads.Monads. Require Import UniMath.CategoryTheory.Monads.KleisliCategory. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.Examples.MonadsLax. Require Import UniMath.Bicategories.Core.Examples.BicatOfCats. Require Import UniMath.Bicategories.Core.Examples.OpMorBicat. Require Import UniMath.Bicategories.Monads.Examples.MonadsInBicatOfCats. Require Import UniMath.Bicategories.Monads.Examples.MonadsInOp1Bicat. Require Import UniMath.Bicategories.Colimits.KleisliObjects.