Definition functor_from_kleisli_cat_monad_nat_trans : Left_Kleisli_functor m ∙ functor_from_kleisli_cat_monad ⟹ F. Proof. use make_nat_trans. - exact (λ x, identity _). - abstract (intros x y f ; cbn ; rewrite id_right, id_left ; rewrite functor_comp ; rewrite !assoc' ; etrans ; [ apply maponpaths ; exact (p₁ y) | ] ; apply id_right). 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.Adjunctions.Core. Require Import UniMath.CategoryTheory.Monads.Monads. Require Import UniMath.CategoryTheory.whiskering.