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Simplicial model structures on pro-categories

Thomas Blom and Ieke Moerdijk

Algebraic & Geometric Topology 23 (2023) 3849–3908
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 –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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