Homotopy theory with marked additive categories
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 present the corresponding ∞-categories ob-tained by inverting equivalences. We apply these results to explicitly calculate limits and colimits in these ∞-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.
Additive categories, Marked categories, Model categories
371-416
Bunke, Ulrich
b5755b35-f32f-4ec9-bb46-ded3cfd42faa
Engel, Alexander
fc6fd4f0-2233-498a-8292-d32b7a082aa5
Kasprowski, Daniel
44af11b9-4d22-49f2-a6a3-04009f45b075
Winges, Christoph
347e42cd-fbb9-4dfc-80e3-84c79eb5696a
8 April 2020
Bunke, Ulrich
b5755b35-f32f-4ec9-bb46-ded3cfd42faa
Engel, Alexander
fc6fd4f0-2233-498a-8292-d32b7a082aa5
Kasprowski, Daniel
44af11b9-4d22-49f2-a6a3-04009f45b075
Winges, Christoph
347e42cd-fbb9-4dfc-80e3-84c79eb5696a
Bunke, Ulrich, Engel, Alexander, Kasprowski, Daniel and Winges, Christoph
(2020)
Homotopy theory with marked additive categories.
Theory and Applications of Categories, 35 (13), .
Abstract
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 ∞-categories ob-tained by inverting equivalences. We apply these results to explicitly calculate limits and colimits in these ∞-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.
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More information
Accepted/In Press date: 2 April 2020
Published date: 8 April 2020
Keywords:
Additive categories, Marked categories, Model categories
Identifiers
Local EPrints ID: 478544
URI: http://eprints.soton.ac.uk/id/eprint/478544
ISSN: 1201-561X
PURE UUID: 8c87b713-0aba-4ff1-8212-6f3e4339b6fc
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Date deposited: 04 Jul 2023 17:48
Last modified: 17 Mar 2024 04:19
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Contributors
Author:
Ulrich Bunke
Author:
Alexander Engel
Author:
Daniel Kasprowski
Author:
Christoph Winges
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