{B A A' : AbGroup} (E : AbSES B A) (f : A $-> A') (phi : middle E $-> A') (k : f == phi $o inclusion E) : AbSESMorphism E (pt : AbSES B A'). Proof. srapply (Build_AbSESMorphism f _ grp_homo_id). 1: exact (ab_biprod_corec phi (projection E)). { intro a; cbn. refine (path_prod' (k a) _^). apply isexact_inclusion_projection. } reflexivity. Defined.
Require Import Basics Types Truncations.Core. Require Import WildCat Pointed.Core Homotopy.ExactSequence HIT.epi. Require Import Modalities.ReflectiveSubuniverse. Require Import AbelianGroup AbPushout AbHom AbGroups.Biproduct. Require Import AbSES.Core AbSES.DirectSum.