Homotopy theory with marked additive categories

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 pr...

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Bibliographic Details
Published inTheory and applications of categories Vol. 35; no. 13; p. 371
Main Authors Bunke, Ulrich, Engel, Alexander, Kasprowski, Daniel, Winges, Christoph
Format Journal Article
LanguageEnglish
Published Sackville R. Rosebrugh 01.01.2020
Subjects
Algebraic group theory
Categories
Classification
Combinatorial analysis
Combinatorics
Construction
Homology
Homotopy theory
Infinity
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Summary: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.
ISSN:1201-561X