Combinatorial model categories have presentations

2000/07/11 by Daniel Dugger, Dugger, Daniel · 3 citations
Mathematics · #Algebraic Topology (math.AT) #FOS: Mathematics #math.AT

paper · pdf · doi:10.48550/arxiv.math/0007068

arxiv created 2000/07/11 · arxiv updated 2009/11/30

Abstract

We show that every combinatorial model category can be obtained, up to Quillen equivalence, by localizing a model category of diagrams of simplicial sets. This says that any combinatorial model category can be built up from a category of `generators' and a set of `relations'---that is, any combinatorial model category has a presentation.

Cited by

• Models for rational (∞, 1)-categories
• Chern character for torsion-free ample groupoids
• A modern perspective on rational homotopy theory

Related

• Small presentations of model categories and Vopěnka's principle
• A model category structure on the category of simplicial multicategories
• Model category structures on simplicial objects
• Model Categories and Simplicial Methods
• Constructing model categories with prescribed fibrant objects