Sheafifiable homotopy model categories

2000/11/01 by Tibor Beke · 7 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · #Algebraic structures and combinatorial models #Homotopy #Homotopy and Cohomology in Algebraic Topology #Mathematics #Pure mathematics #Sphingolipid Metabolism and Signaling #math.AT #math.CT #msc:18F10 #msc:18G55

paper · pdf · doi:10.1017/s0305004100004722

published as Mathematical Proceedings of the Cambridge Philosophical Society, vol.129, no.3, pp.447-475, 2000 · 30 pages

openalex publication_date 2000/11/01 · arxiv created 2001/02/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

If a Quillen model category can be specified using a certain logical syntax (intuitively, ‘is algebraic/combinatorial enough’), so that it can be defined in any category of sheaves, then the satisfaction of Quillen's axioms over any site is a purely formal consequence of their being satisfied over the category of sets. Such data give rise to a functor from the category of topoi and geometric morphisms to Quillen model categories and Quillen adjunctions.

Citations

• Accessible Categories: The Foundations of Categorical Model Theory
• Rings and Modules of Quotients
• Simplicial Homotopy Theory

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• Algebraic models for equivariant rational homotopy theory for discrete groups
• Categorical Homotopy Theory
• Equivariant dendroidal Segal spaces andG–∞–operads
• Comparison Between Different Topological Models of Concurrency
• Quillen-Segal algebras and Stable homotopy theory
• The Brown-Golasiński model structure on strict ∞-groupoids revisited
• Homotopy category [wikipedia]