Lemma AdditiveFunctorUnel {A B : CategoryWithAdditiveStructure} (F : AdditiveFunctor A B) (a1 a2 : A) : # F (to_unel a1 a2) = to_unel (F a1) (F a2). Proof. unfold to_unel. apply (pr2 (pr2 F a1 a2)). Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.Algebra.BinaryOperations. Require Import UniMath.Algebra.Monoids. Require Import UniMath.Algebra.Groups. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.CategoriesWithBinOps. Require Import UniMath.CategoryTheory.PrecategoriesWithAbgrops. Require Import UniMath.CategoryTheory.PreAdditive. Require Import UniMath.CategoryTheory.Additive. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.Limits.Zero. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Require Import UniMath.CategoryTheory.Limits.BinDirectSums. exists (ZeroArrowFrom (F (to_Zero A))). apply ArrowsFromZero. assert (e2 : # F (ZeroArrowFrom a2) = @ZeroArrowFrom B Z (F a2)). apply (ArrowsFromZero B Z). use (FromBinDirectSumsEq B BDS); cbn.