Simplicial model structures on pro-categories
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Simplicial model structures on pro-categories. / Blom, Thomas; Moerdijk, Ieke.
In: Algebraic & Geometric Topology, Vol. 23, No. 8, 2023, p. 3849-3908.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Simplicial model structures on pro-categories
AU - Blom, Thomas
AU - Moerdijk, Ieke
PY - 2023
Y1 - 2023
N2 - 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.
AB - 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.
U2 - 10.2140/agt.2023.23.3849
DO - 10.2140/agt.2023.23.3849
M3 - Journal article
VL - 23
SP - 3849
EP - 3908
JO - Algebraic and Geometric Topology
JF - Algebraic and Geometric Topology
SN - 1472-2747
IS - 8
ER -
ID: 373794437