Grothendieck topologies from unique factorisation systems

Abstract

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.

version 2, completed some proofs, change some references

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