Geodesic
Axiomatic Proof of J. Lambek's Homological Theorem
Canadian mathematical bulletin, Tome 7 (1964) no. 4, pp. 609-613

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A category with zero-maps is called "quasi-exact" in the sense of D. Puppe (see [4], 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 [3], page 252, (1. 10) and (1. 11)). 
Leicht, J. B. Axiomatic Proof of J. Lambek's Homological Theorem. Canadian mathematical bulletin, Tome 7 (1964) no. 4, pp. 609-613. doi: 10.4153/CMB-1964-056-4
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     title = {Axiomatic {Proof} of {J.} {Lambek's} {Homological} {Theorem}},
     journal = {Canadian mathematical bulletin},
     pages = {609--613},
     year = {1964},
     volume = {7},
     number = {4},
     doi = {10.4153/CMB-1964-056-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1964-056-4/}
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