Grothendieck topologies from unique factorisation systems
Algebraic Geometry
2009-10-22 v2 Category Theory
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.
Cite
@article{arxiv.0902.1130,
title = {Grothendieck topologies from unique factorisation systems},
author = {Mathieu Anel},
journal= {arXiv preprint arXiv:0902.1130},
year = {2009}
}
Comments
version 2, completed some proofs, change some references