Definition pre_whisker {A B C : enriched_precat} (F : enriched_functor A B) {G H : enriched_functor B C} (a : enriched_nat_trans G H) : enriched_nat_trans (enriched_functor_comp F G) (enriched_functor_comp F H). Proof. use make_enriched_nat_trans. - intro x. exact (a (F x)). - abstract (intros x y; simpl; rewrite !assoc'; apply cancel_precomposition; 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.