Simplicial model structures on pro-categories

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.