  This work presents a way to associate a Grothendieck site structure to a
category endowed with a unique factorisation system of its arrows. In
particular this recovers the Zariski and Etale topologies and others related to
Voevodsky's cd-structures. As unique factorisation systems are also frequent
outside algebraic geometry, a construction applies to some new contexts, where
it is related with known structures defined otherwise. The paper details
algebraic geometrical situations and sketches only the other contexts.
