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Axiomatic Proof of J. Lambek's Homological Theorem

Published online by Cambridge University Press:  20 November 2018

J. B. Leicht
J. B. Leicht*
Affiliation:
University of Toronto
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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:

  1. (Q1) Every may f is a product f=με of an epimorphisrn εfollowed by a monomorphism μ

  1. (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)).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 7 , Issue 4 , December 1964 , pp. 609 - 613
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Hilton, P. J., Lederman., W., Homology and Ringoids III, Proceedings of the Cambridge Philosophical Society Vol. 56 (1960), 1–12.CrossRefGoogle Scholar
2. Leicht, J.B., Űber die elementaren Lemmata der homoiogischen Algebra in quasi-exacten Kategorien, Monatshefte der Mathematik. Forthcoming.Google Scholar
3. MacLane., S., Homology, Grundlehren der Mathematischen Wissenschaften Bd. 114, Springer-Verlag (1963).Google Scholar
4. Puppe., D., Korrespondenzen űber abelschen Kategorien, Mathematische Annalen Bd. 148 (1963), Seite 1–30.Google Scholar