Definition product_precategory_data : precategory_data. Proof. exists product_precategory_ob_mor. split. - intros f i; simpl in *. apply (identity (f i)). - intros a b c f g i; simpl in *. exact (f i · g i). Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.opp_precat.