Lemma is_functor_bincoproduct_functor_data {C : category} (PC : BinCoproducts C) : is_functor (bincoproduct_functor_data PC). Proof. split. - intro x; simpl; apply pathsinv0. use BinCoproduct_endo_is_identity. + now rewrite BinCoproductOfArrowsIn1, id_left. + now rewrite BinCoproductOfArrowsIn2, id_left. - now intros x y z f g; simpl; rewrite BinCoproductOfArrows_comp. Qed.
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.