Lemma univ_arrow_mor_assoc {C:category} {a b:C} {Z:[C^op,HSET]} (f : a --> b) (z : b ⇒ Z) (t : Representation Z) : (t \\ z) ∘ f = t \\ (z ⟲ f). Proof. apply universalMapUniqueness. unshelve refine (arrow_mor_mor_assoc _ _ _ @ _). apply maponpaths. apply universalMapProperty. Qed.
Require Import UniMath.Foundations.Preamble. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import Require Import Require Import UniMath.MoreFoundations.Tactics.