Definition post_whisker {A B C : enriched_precat} {F G : enriched_functor A B} (a : enriched_nat_trans F G) (H : enriched_functor B C) : enriched_nat_trans (enriched_functor_comp F H) (enriched_functor_comp G H). Proof. use make_enriched_nat_trans. - intro x. exact (a x · enriched_functor_on_morphisms H _ _). - abstract (intros x y; simpl; rewrite !assoc'; rewrite <- enriched_functor_on_precompose, <- enriched_functor_on_postcompose; rewrite !assoc; apply cancel_postcomposition; apply enriched_nat_trans_ax). Defined.
Require Import UniMath.Foundations.PartA. Require Import UniMath.Foundations.Propositions. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.Core.Isos. Import MonoidalNotations.