$t$-model structures

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

Full Text (PDF format)

Published 1 January 2007