Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-27T01:37:36.379Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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