Definition co_eilenberg_moore_nat_trans {C : category} (m : Comonad C) : functor_identity _ ∙ co_eilenberg_moore_pr m ⟹ co_eilenberg_moore_pr m ∙ m. Proof. use make_nat_trans. - exact (λ f, mor_of_co_eilenberg_moore_ob f). - abstract (intros f₁ f₂ α ; cbn ; exact (!(eq_of_co_eilenberg_moore_mor α))). 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.Core.Univalence. Require Import UniMath.CategoryTheory.Categories.Dialgebras. Require Import UniMath.CategoryTheory.Subcategory.Core. Require Import UniMath.CategoryTheory.Subcategory.Full. Require Import UniMath.CategoryTheory.Monads.Comonads.