Homology, Homotopy and Applications

Volume 9 (2007)

Number 1

$t$-model structures

Pages: 399 – 438

DOI: https://dx.doi.org/10.4310/HHA.2007.v9.n1.a16


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

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


For every stable model category $\mathcal{M}$ with a certain extra structure, we produce an associated model structure on the pro-category pro-$\mathcal{M}$ and a spectral sequence, analogous to the Atiyah-Hirzebruch spectral sequence, with reasonably good convergence properties for computing in the homotopy category of pro-$\mathcal{M}$. Our motivating example is the category of pro-spectra.

The extra structure referred to above is a $t$-model structure. This is a rigidification of the usual notion of a $t$-structure on a triangulated category. A $t$-model structure is a proper simplicial stable model category $\mathcal{M}$ with a $t$-structure on its homotopy category together with an additional factorization axiom.


model category, pro-category, $t$-structure

2010 Mathematics Subject Classification

18E30, 55P42, 55U35

Published 1 January 2007