Lemma productMapUniqueness {C:category} {I} {c:I -> ob C} (prod : Product c) {a:C} (f g : Hom C a (universalObject prod)) : (∏ i, pr_ prod i ∘ f = pr_ prod i ∘ g) -> f = g. Proof. intro e. apply mapUniqueness. apply funextsec; intro i. apply e. Defined.
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.