Homotopy theory with marked additive categories

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

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Journal Article

Homotopy theory with marked additive categories

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Winges, Christoph
Max Planck Institute for Mathematics, Max Planck Society;

External Ressource

http://www.tac.mta.ca/tac/volumes/35/13/35-13.pdf
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arXiv:1811.04007.pdf
(Preprint), 569KB

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Citation

Bunke, U., Engel, A., Kasprowski, D., & Winges, C. (2020). Homotopy theory with marked additive categories. Theory and Applications of Categories, 35: 13, pp. 371-416.

Cite as: http://hdl.handle.net/21.11116/0000-0006-9256-4

Abstract

We construct combinatorial model category structures on the categories of (marked) categories and (marked) pre-additive categories, and we characterize (marked) additive categories as fibrant objects in a Bousfield localization of pre-additive categories. These model category structures are used to present the corresponding $\infty$-categories obtained by inverting equivalences. We apply these results to explicitly calculate various limits and colimits in these $\infty$-categories.