Definition Kleisli_cat_monad_enrichment_data : enrichment_data (Kleisli_cat_monad M) V. Proof. simple refine (_ ,, _ ,, _ ,, _ ,, _). - exact (λ x y, E ⦃ x , M y ⦄). - exact (λ x, enriched_from_arr E (η M x)). - exact (λ x y z, endo_of_monad_enrichment EM y (M z) #⊗ identity _ · enriched_comp E x (M y) (M(M z)) · postcomp_arr E x (μ M z)). - exact (λ x y f, enriched_from_arr E f). - exact (λ x y f, enriched_to_arr E f). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentFunctor. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentTransformation. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentMonad. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monads.Monads. Require Import UniMath.CategoryTheory.Monads.KleisliCategory. Section FunctorFromKleisli. End FunctorFromKleisli.