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Model category structures on multicomplexes

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  • X. Fu
  • A. Guan
  • M. Livernet
  • S. Whitehouse
Article number108104
<mark>Journal publication date</mark>1/07/2022
<mark>Journal</mark>Topology and its Applications
Number of pages26
Publication StatusPublished
Early online date13/06/22
<mark>Original language</mark>English


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.