Definition bicat_of_enriched_cats_has_kleisli_cocone : kleisli_cocone EM. Proof. use make_kleisli_cocone. - exact (univalent_kleisli_cat M ,, kleisli_cat_enrichment HV EM'). - exact (kleisli_incl M ,, kleisli_incl_enrichment HV EM'). - exact (kleisli_nat_trans M ,, kleisli_nat_trans_enrichment HV EM'). - abstract (use eq_enriched_nat_trans ; intro x ; use eq_mor_kleisli_cat ; exact (@Monad_law2 _ M x)). - abstract (use eq_enriched_nat_trans ; intro x ; use eq_mor_kleisli_cat ; cbn ; rewrite id_left ; apply (!(@Monad_law3 _ M x))). Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Categories.KleisliCategory. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentMonad. Require Import UniMath.CategoryTheory.EnrichedCats.Examples.UnivalentKleisliEnriched. Require Import UniMath.CategoryTheory.EnrichedCats.Examples.UnivalentKleisliMapping. Require Import UniMath.CategoryTheory.Monads.Monads. Require Import UniMath.CategoryTheory.Limits.Equalizers. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Examples.OpMorBicat. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.Examples.EnrichedCats. Require Import UniMath.Bicategories.DisplayedBicats.Examples.MonadsLax. Require Import UniMath.Bicategories.Monads.Examples.MonadsInBicatOfEnrichedCats. Require Import UniMath.Bicategories.Monads.Examples.MonadsInOp1Bicat. Require Import UniMath.Bicategories.Colimits.KleisliObjects.