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# Homology, Homotopy and Applications

## Volume 9 (2007)

### Number 1

### $t$-model structures

Pages: 399 – 438

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

#### Authors

#### Abstract

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.

#### Keywords

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

#### 2010 Mathematics Subject Classification

18E30, 55P42, 55U35