Definition bincoproduct_functor_data {C : category} (PC : BinCoproducts C) : functor_data (category_binproduct C C) C. Proof. use tpair. - intros p. apply (BinCoproductObject (PC (pr1 p) (pr2 p))). - intros p q f. apply (BinCoproductOfArrows _ (PC (pr1 p) (pr2 p)) (PC (pr1 q) (pr2 q)) (pr1 f) (pr2 f)). 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.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.Limits.Zero. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.Limits.Coproducts. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.ProductCategory.