Definition free_Algebra (X : C) : Algebra. Proof. use tpair. - exists (T X). exact (μ T X). - abstract (split; [apply Monad_law1 | apply pathsinv0; apply Monad_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.Monads. Require Import UniMath.CategoryTheory.Monads.Derivative.