English

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.

Keywords

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

R2 v1 2026-06-21T12:08:42.476Z