Model category structures on multicomplexes

Xin Fu; Ai Guan; Muriel Livernet; Sarah Whitehouse

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arXiv · 2001.10873

Model category structures on multicomplexes

Xin Fu·Ai Guan·Muriel Livernet·Sarah Whitehouse

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Abstract

We present a family of model structures on the category of multicomplexes. There is a cofibrantly generated model structure in which the weak equivalences are the morphisms inducing an isomorphism at a fixed stage of an associated spectral sequence. Corresponding model structures are given for truncated versions of multicomplexes, interpolating between bicomplexes and multicomplexes. For a fixed stage of the spectral sequence, the model structures on all these categories are shown to be Quillen equivalent.

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Xin Fu, Ai Guan, Muriel Livernet, Sarah Whitehouse. 2020-01-29. Model category structures on multicomplexes. https://arxiv.org/abs/2001.10873

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