Definition make_isAdditiveFunctor {A B : CategoryWithAdditiveStructure} (F : functor A B) (H : ∏ (a1 a2 : A), @ismonoidfun (to_abgr a1 a2) (to_abgr (F a1) (F a2)) (# F)) : isAdditiveFunctor F.
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.