Definition hcomp_functor_data : functor_data (category_binproduct (hom a b) (hom b c)) (hom a c). Proof. exists (λ p : (a-->b) × (b-->c), pr1 p · pr2 p). unfold hom_ob_mor. simpl. intros (f1, f2) (g1, g2). unfold precategory_binproduct_mor. simpl. intros (x, y). apply hcomp; assumption. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.PrecategoryBinProduct.