Definition HomFamily (C:category) {I} (c:I -> ob C) : C^op ⟶ SET. Proof. unshelve refine (_,,_). - unshelve refine (_,,_). + intros x. exact (∏ i, Hom C x (c i)) % set. + intros x y f p i; simpl; simpl in p. exact (compose (C:=C) f (p i)). - abstract (split; [ intros a; apply funextsec; intros f; apply funextsec; intros i; simpl; apply id_left | intros x y z p q; apply funextsec; intros f; apply funextsec; intros i; simpl; apply pathsinv0, assoc]) using _L_. 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.