One-sided exact categories

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 3×3 Lemma, can be proved in our context. We also note that the derived category of a one-sided exact additive category can be constructed.