Grothendieck topologies from unique factorisation systems

2009/02/06 by Mathieu Anel, Anel, Mathieu · 4 citations
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.0902.1130

openalex publication_date 2009/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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