Homology, Homotopy and Applications

Volume 9 (2007)

Number 1

Model structures on pro-categories

Pages: 367 – 398

DOI: https://dx.doi.org/10.4310/HHA.2007.v9.n1.a15


Halvard Fausk (Department of Mathematical Sciences, NTNU, Trondheim, Norway)

Daniel C. Isaksen (Department of Mathematics, Wayne State University, Detroit, Michigan, U.S.A.)


We introduce a notion of a filtered model structure and use this notion to produce various model structures on procategories. We give several examples, including a homotopy theory for $G$-spaces, where $G$ is a profinite group. The class of weak equivalences are an approximation to the class of underlying weak equivalences.


model category, pro-category

2010 Mathematics Subject Classification

Primary 55U35. Secondary 18G55, 55P91.

Published 1 January 2007