Lemma LModule_same_func_Mor_laws {m1 m2 : R ∙ F ⟹ F } (hm : ∏ c, m1 c = m2 c) : LModule_Mor_laws R (T := (F ,, m1)) (T' := (F ,, m2)) (nat_trans_id _). Proof. intro c. etrans;[apply id_left|]. apply pathsinv0. etrans;[apply ( (id_right _))|]. apply hm. Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Require Import UniMath.CategoryTheory.Monads.Monads.