Lemma transport_compose {C : precategory} {x y z w : ob C} (f : x --> y) (g : z --> w) (e : y = z) : transportf (precategory_morphisms x) e f · g = f · transportf (λ x' : ob C, precategory_morphisms x' w) (! e) g. Proof. induction e. apply idpath. Qed.
Require Import UniMath.Foundations.PartA. Require Import UniMath.Foundations.UnivalenceAxiom. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos.