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.