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The model structure on the category of chain functors Ch, developed in [4], has the main features of a simplicial model category structure, taking into account the lack of arbitrary (co-)limits in Ch. After an appropriate tensor and cotensor structure in 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 Ch with the structure of an approximate simplicial stable model structure (= approximate ss-model structure) (§7). In §8 the model structure on Ch is shown to be proper.

Simplicial model category structures on the category of chain functors