Definition AddEquivUnit {A1 A2 : CategoryWithAdditiveStructure} (AE : AddEquiv A1 A2) : nat_trans (functor_identity A1) (functor_composite (AddEquiv1 AE) (AddEquiv2 AE)) := unit_from_left_adjoint AE.
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.