One-sided exact categories

Details One-sided exact categories One-sided exact categories

2011-06-06

arxiv.org/abs/1106.1092v1

Mathematics

Category Theory

Scientific paper

One-sided exact categories appear naturally as instances of Grothendieck pretopologies. In an additive setting they are given by considering the one-sided part of Keller's axioms defining Quillen exact categories. We study one-sided exact additive categories and a stronger version defined by adding the one-sided part of Quillen "obscure axiom". We show that some homological results, such as the Short Five Lemma and the 3 X 3 Lemma, can be proved in our context. We also note that the derived category of a one-sided exact additive category can be constructed.

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