Definition Coalgebra_laws (X : Coalgebra_data) : UU := (Coalg_map X · ε T X = identity X) × (Coalg_map X · δ T X = Coalg_map X · #T (Coalg_map X)).
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.