A "working mathematician's" definition of semi-abelian categories

Details A "working mathematician's" definition of semi-abelian categories A "working mathematician's" definition of semi-abelian categories

2009-05-29

arxiv.org/abs/0905.4941v2

Mathematics

Category Theory

11 pages

Scientific paper

Semi-abelian and finitely cocomplete homological categories are characterized in terms of four resp. three simple axioms, in terms of the basic categorical notions introduced in the first few chapters of MacLane's classical book. As an immediate application we show that categories of diagrams in semi-abelian and similar categories are of the same type; in particular, the category of simplicial or \Gamma-objects in a semi-abelian category is semi-abelian.

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