Definition enriched_functor_from_univalent_kleisli_cat : enriched_functor_category (kleisli_cat_enrichment HV EM) E' := lift_enriched_functor_along _ (essentially_surjective_functor_to_kleisli_cat M) (fully_faithful_functor_to_kleisli_cat_enrichment HV EM) LL.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.Categories.EilenbergMoore. Require Import UniMath.CategoryTheory.Categories.KleisliCategory. 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.EnrichedCats.Examples.KleisliEnriched. Require Import UniMath.CategoryTheory.EnrichedCats.Examples.UnivalentKleisliEnriched. Require Import UniMath.CategoryTheory.EnrichedCats.Examples.FunctorCategory. Require Import UniMath.CategoryTheory.EnrichedCats.RezkCompletion.RezkUniversalProperty. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monads.Monads. Require Import UniMath.CategoryTheory.Monads.KleisliCategory. Require Import UniMath.CategoryTheory.Limits.Equalizers. Section FunctorFromUnivalentKleisli. End FunctorFromUnivalentKleisli. Section NatTransFromUnivalentKleisli. End NatTransFromUnivalentKleisli.