Simplicial model structures on pro-categories

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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.
Original languageEnglish
JournalAlgebraic & Geometric Topology
Volume23
Issue number8
Pages (from-to)3849-3908
ISSN1472-2747
DOIs
Publication statusPublished - 2023

ID: 373794437