T-model structures

Details T-model structures T-model structures

2005-11-02

arxiv.org/abs/math/0511056v2

Mathematics

Algebraic Topology

36 pages

Scientific paper

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.

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