Definition functor_to_eilenberg_moore_cat_data : functor_data C₁ (eilenberg_moore_cat m). Proof. use make_functor_data. - intro x. use make_ob_eilenberg_moore. + exact (F x). + exact (α x). + exact (αη x). + exact (!(αμ x)). - intros x y f. use make_mor_eilenberg_moore. + exact (#F f). + exact (!(nat_trans_ax α _ _ f)). 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.Monads.