Model category structures on multicomplexes

Fu, X. and Guan, A. and Livernet, M. and Whitehouse, S. (2022) Model category structures on multicomplexes. Topology and its Applications, 316: 108104.

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.