Geodesic
Simplicial model structures on pro-categories
Blom, Thomas1 ; Moerdijk, Ieke2
1 Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark
2 Mathematisch Instituut, Universiteit Utrecht, Utrecht, Netherlands
Algebraic and Geometric Topology, Tome 23 (2023) no. 8, pp. 3849-3908

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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.

DOI : 10.2140/agt.2023.23.3849
Keywords: pro-categories, Quillen model structures, fibration test category, profinite spaces, profinite infinity-categories

Blom, Thomas 1 ; Moerdijk, Ieke 2

1 Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark
2 Mathematisch Instituut, Universiteit Utrecht, Utrecht, Netherlands 
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Blom, Thomas; Moerdijk, Ieke. Simplicial model structures on pro-categories. Algebraic and Geometric Topology, Tome 23 (2023) no. 8, pp. 3849-3908. doi: 10.2140/agt.2023.23.3849

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