Definition coproduct_functor (I : UU) {C : category} (PC : Coproducts I C) : functor (power_category I C) C. Proof. apply (tpair _ (coproduct_functor_data _ PC)). abstract (split; [intro x; simpl; apply pathsinv0, Coproduct_endo_is_identity; now intro i; rewrite CoproductOfArrowsIn, id_left | now intros x y z f g; simpl; rewrite CoproductOfArrows_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.whiskering.