Homology, Homotopy and Applications

Volume 9 (2007)

Number 1

Simplicial model category structures on the category of chain functors

Pages: 107 – 138

DOI: http://dx.doi.org/10.4310/HHA.2007.v9.n1.a4

Authors

Friedrich W. Bauer (Fachbereich Mathematik, Johann Wolfgang Goethe Universität, Frankfurt a.M., Germany)

Tamar Datuashvili (A. Razmadze Mathematical Institute, Georgian Academy of Sciences, Tbilisi, Republic of Georgia)

Abstract

The model structure on the category of chain functors $\mathfrak{Ch}$, developed in [4], has the main features of a simplicial model category structure, taking into account the lack of arbitrary (co-)limits in $\mathfrak{Ch}$. After an appropriate tensor and cotensor structure in $\mathfrak{Ch}$ is established (§1, §3), Quillen's axiom SM7 is verified in §5 and §6. Moreover, it turns out that in the definition of a simplicial model structure, the category of simplicial sets can be replaced by the category of simplicial spectra endowing $\mathfrak{Ch}$ with the structure of an approximate simplicial stable model structure (= approximate ss-model structure) (§7). In §8 the model structure on $\mathfrak{Ch}$ is shown to be proper.

Keywords

chain functor; simplicial spectrum; fibration; cofibration

2010 Mathematics Subject Classification

18G35, 55U15, 55U35, 55U40

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