Definition productMapExistence {C:category} {I} {c:I -> ob C} (prod : Product c) {a:C} : (∏ i, Hom C a (c i)) -> Hom C a (universalObject prod) := λ f, prod \\ f.
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.