Definition eq2 (T' : Monad (MonadAlg S))(e : lift_eq T') : functor_composite_data (forget_Alg S) (functor_composite_data T T) = functor_composite_data (functor_composite_data T' T') (forget_Alg S). Proof. apply (pathscomp0 (maponpaths (fun X => functor_composite_data X T) e)). exact (maponpaths (functor_composite_data T') e). 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.