A category with zero-maps is called "quasi-exact" in the sense of D. Puppe (see , page 8, 2. 4), if it satisfies the following axioms:
(Q1)Every may f is a product f=με of an epimorphisrn εfollowed by a monomorphism μ
(Q2)a) Every epimorphism ε has a kernel k = ker ε
b) Every monomorphism μ has a cokernel γ = Coker ε, where Ker and Coker are characterized by the familiar universality properties (see , page 252, (1. 10) and (1. 11)).