Corollary functorial_composition_legacy_ok {A B C : category} : functorial_composition_legacy A B C = functorial_composition _ _ _. Proof. apply functor_eq. - apply homset_property. - cbn. use functor_data_eq. + intro FG. apply idpath. + intros FG1 FG2 αβ. cbn. apply (horcomp_post_pre _ _ C). Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.UnitorsAndAssociatorsForEndofunctors.