Definition unit_mu_kleisli : monad bicat_of_univ_cats x. Proof. use make_cat_monad. - exact (functor_of_kleisli_triple k). - exact (unit_kleisli k). - exact (mu_kleisli k). - abstract (cbn; intros; rewrite (bind_bind k); rewrite assoc'; rewrite (unit_bind k); rewrite id_right; apply (bind_unit k)). - abstract (cbn; intros; apply (unit_bind k)). - abstract (cbn; intros; do 2 rewrite (bind_bind k); rewrite id_left; apply maponpaths; rewrite assoc'; rewrite (unit_bind k); rewrite id_right; apply idpath). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Import PseudoFunctor.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispAdjunctions. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Require Import UniMath.Bicategories.PseudoFunctors.Examples.Identity. Require Import UniMath.Bicategories.PseudoFunctors.Examples.Composition. Require Import UniMath.Bicategories.PseudoFunctors.Examples.Projection. Require Import UniMath.Bicategories.Transformations.PseudoTransformation. Require Import UniMath.Bicategories.Transformations.Examples.AlgebraMap. Require Import UniMath.Bicategories.Modifications.Modification. Require Import UniMath.Bicategories.PseudoFunctors.Biequivalence. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.DisplayedBicats.DispPseudofunctor. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Algebras. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Add2Cell. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Prod. Require Import UniMath.Bicategories.DisplayedBicats.Examples.FullSub. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Monads. Require Import UniMath.Bicategories.DisplayedBicats.Examples.KleisliTriple. Require Import UniMath.Bicategories.DisplayedBicats.DispBuilders. Require Import UniMath.Bicategories.DisplayedBicats.DispTransformation. Require Import UniMath.Bicategories.DisplayedBicats.DispModification. Require Import UniMath.Bicategories.DisplayedBicats.DispBiequivalence. Require Import UniMath.Bicategories.Transformations.Examples.Unitality. Require Import UniMath.Bicategories.DisplayedBicats.Examples.KleisliTriple. Require Import UniMath.CategoryTheory.Equivalences.CompositesAndInverses.