Simplicial model category structures on the category of chain functors

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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Published 1 January 2007