Definition K_0_hrel (M:ExactCategory) : hrel (free_abgr (π₀ (ob M))) := λ g h, ∃ E : ShortExactSequence M, g = free_abgr_unit (component (Ob2 E)) × h = free_abgr_unit (component (Ob1 E)) + free_abgr_unit (component (Ob3 E)).
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.Algebra.Groups. Require Import UniMath.Algebra.Free_Monoids_and_Groups.