Definition product_functor : functor (power_category I C) C. Proof. apply (tpair _ product_functor_data). abstract (split; [ now intro x; simpl; apply pathsinv0, Product_endo_is_identity; intro i; rewrite ProductOfArrowsPr, id_right | now intros x y z f g; simpl; rewrite ProductOfArrows_comp]). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.ProductCategory. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.Limits.Graphs.Limits. Require Import UniMath.Combinatorics.StandardFiniteSets. Section ProductFromIso. End ProductFromIso.