Geodesic
Homotopy theory with marked additive categories
Theory and applications of categories, Tome 35 (2020), pp. 371-416

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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.

Publié le :
Classification : 18E05, 18N40
Keywords: Additive categories, marked categories, model categories 
@article{TAC_2020_35_a12,
     author = {Ulrich Bunke and Alexander Engel and Daniel Kasprowski and Christoph Winges},
     title = {Homotopy theory with marked additive categories},
     journal = {Theory and applications of categories},
     pages = {371--416},
     publisher = {mathdoc},
     volume = {35},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2020_35_a12/}
}
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Ulrich Bunke; Alexander Engel; Daniel Kasprowski; Christoph Winges. Homotopy theory with marked additive categories. Theory and applications of categories, Tome 35 (2020), pp. 371-416. http://geodesic.mathdoc.fr/item/TAC_2020_35_a12/