Definition free_Coalgebra (X : C) : Coalgebra. Proof. use tpair. - exists (T X). exact (δ T X). - abstract (split; [apply Comonad_law1 | apply pathsinv0; apply Comonad_law3]). Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Monads.Comonads.