Grothendieck topologies from unique factorisation systems

Details Grothendieck topologies from unique factorisation systems Grothendieck topologies from unique factorisation systems

2009-02-06

arxiv.org/abs/0902.1130v2

Mathematics

Algebraic Geometry

version 2, completed some proofs, change some references

Scientific paper

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.

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