Lemma transport_compose' {C : precategory} {x y z w : ob C} (f : x --> y) (g : y --> z) (e : y = w) : (transportf (precategory_morphisms x) e f) · (transportf (λ x' : ob C, precategory_morphisms x' z) e g) = f · 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.