Definition make_Coalgebra_data {C : category} (T : Comonad C) (X : C) (α : X --> T X) : Coalgebra_data T. Proof. use tpair. - exact X. - exact α. Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Monads.Monads. Require Import UniMath.CategoryTheory.Monads.MonadAlgebras. Require Import UniMath.CategoryTheory.Monads.Comonads. Require Import UniMath.CategoryTheory.Monads.ComonadCoalgebras. Require Import UniMath.CategoryTheory.catiso. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total.