Lemma lax_lineator_postcomp_SelfActCAT_laws : lineator_laxlaws (Mon_endo C) (SelfActCAT C) (SelfActCAT C) (post_comp_functor G) lax_lineator_postcomp_SelfActCAT_data. Proof. split4. - intro; intros. apply (nat_trans_eq C). intro c. cbn. rewrite id_left; apply id_right. - intro; intros. apply (nat_trans_eq C). intro c. cbn. rewrite id_left; apply id_right. - intro; intros. apply (nat_trans_eq C). intro c. cbn. do 3 rewrite id_left. apply functor_id. - intro; intros. apply (nat_trans_eq C). intro c. cbn. rewrite id_left. apply functor_id. Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.BicatOfCatsElementary. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Examples.EndofunctorsMonoidalElementary. Require Import UniMath.CategoryTheory.Actegories.Examples.ActionOfEndomorphismsInCATElementary. Require Import UniMath.CategoryTheory.Actegories.Actegories. Require Import UniMath.CategoryTheory.Actegories.ConstructionOfActegories. Require Import UniMath.CategoryTheory.Actegories.MorphismsOfActegories. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Require Import UniMath.CategoryTheory.Limits.Coproducts. Require Import UniMath.CategoryTheory.Actegories.CoproductsInActegories.