  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.
