Lemma BinCoproductArrow_eq_cor (f f' : BinCoproductObject (CC a b) --> c) : BinCoproductIn1 _· f = BinCoproductIn1 _· f' → BinCoproductIn2 _· f = BinCoproductIn2 _· f' → f = f' . Proof. intros Hyp1 Hyp2. rewrite (BinCoproductArrowEta _ _ _ _ _ f). rewrite (BinCoproductArrowEta _ _ _ _ _ f'). apply maponpaths_12; assumption. 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.