Simplicial model structures on pro-categories

Blom, Thomas; Moerdijk, Ieke

doi:10.2140/agt.2023.23.3849

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Simplicial model structures on pro-categories

Thomas Blom and Ieke Moerdijk

Algebraic & Geometric Topology 23 (2023) 3849–3908

DOI: 10.2140/agt.2023.23.3849

Abstract

We describe a method for constructing simplicial model structures on ind- and pro-categories. Our method is particularly useful for constructing “profinite” analogues of known model categories. Our construction quickly recovers Morel’s model structure for pro- $p$ spaces and Quick’s model structure for profinite spaces, but we will show that it can also be applied to construct many interesting new model structures. In addition, we study some general properties of our method, such as its functorial behavior and its relation to Bousfield localization. We compare our construction to the $\infty$ –categorical approach to ind- and pro-categories in an appendix.

Keywords

pro-categories, Quillen model structures, fibration test category, profinite spaces, profinite infinity-categories

Mathematical Subject Classification

Primary: 55U35

Secondary: 18N40

References

Publication

Received: 24 May 2022

Accepted: 26 July 2022

Published: 5 November 2023

Authors

Thomas Blom
Department of Mathematical Sciences University of Copenhagen Copenhagen Denmark

Ieke Moerdijk
Mathematisch Instituut Universiteit Utrecht Utrecht Netherlands

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Volume 23, issue 8 (2023)