Homotopy theory with marked additive categories

Ulrich Bunke, Alexander Engel, Daniel Kasprowski, and Christoph Winges

We construct combinatorial model category structures on the categories of (marked) categories and (marked) preadditive categories, and we characterize (marked) additive categories as fibrant objects in a Bousfield localization of preadditive categories. These model category structures are used to present the corresponding infinity-categories obtained by inverting equivalences. We apply these results to explicitly calculate limits and colimits in these infinity-categories. The motivating application is a systematic construction of the equivariant coarse algebraic K-homology with coefficients in an additive category from its non-equivariant version.

Keywords: Additive categories, marked categories, model categories

2020 MSC: 18E05, 18N40

Theory and Applications of Categories, Vol. 35, 2020, No. 13, pp 371-416.

Published 2020-04-08.


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