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's exact categories. We study one-sided exact additive categories and a stronger version defined by adding the one-sided part of Quillen's ``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.
One-sided exact categories
BAZZONI, SILVANA;
2013
Abstract
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's exact categories. We study one-sided exact additive categories and a stronger version defined by adding the one-sided part of Quillen's ``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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