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T-model structures

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Halvard Fausk, Daniel C. Isaksen

Algebraic Topology · Submitted 2 Nov 2005

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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-$\mathcal{M}$.

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arXiv IDmath/0511056 (version 2)
Pith IDJ7QIFLMY, Pith's permanent record of this paper and its review
CitationDaniel C. Isaksen, Halvard Fausk. "T-model structures." arXiv:math/0511056 (2005). https://pith.science/paper/J7QIFLMY
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What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.34 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.58 · mentions code or data availability 0.02.

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arXiv listing abstract v2. Results and the main claim are underlined; .

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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#sentencerolethe authors' own workstates the main conclusionstrength
s0 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-$\mathcal{M}$. contribution 0.92 0.92 0.84 asserted 1.00
s1 Our motivating example is the category of pro-spectra. background 0.67 0.44 0.03 asserted 1.00
s2 The extra structure referred to above is a t-model structure. background 0.63 0.26 0.05 asserted 1.00
s3 This is a rigidification of the usual notion of a t-structure on a triangulated category. background 0.72 0.28 0.04 asserted 1.00
s4 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. background 0.72 0.28 0.05 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.86 · evidence from proof or derivation 1.00.

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Original 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.

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