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Traces in monoidal derivators, and homotopy colimits


Gallauer Alves de Souza, Martin (2014). Traces in monoidal derivators, and homotopy colimits. Advances in Mathematics, 261:26-84.

Abstract

A variant of the trace in a monoidal category is given in the setting of closed monoidal derivators, which is applicable to endomorphisms of fiberwise dualizable objects. Functoriality of this trace is established. As an application, an explicit formula is deduced for the trace of the homotopy colimit of endomorphisms over finite categories in which all endomorphisms are invertible. This result can be seen as a generalization of the additivity of traces in monoidal categories with a compatible triangulation.

Abstract

A variant of the trace in a monoidal category is given in the setting of closed monoidal derivators, which is applicable to endomorphisms of fiberwise dualizable objects. Functoriality of this trace is established. As an application, an explicit formula is deduced for the trace of the homotopy colimit of endomorphisms over finite categories in which all endomorphisms are invertible. This result can be seen as a generalization of the additivity of traces in monoidal categories with a compatible triangulation.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2014
Deposited On:27 Jan 2015 16:07
Last Modified:08 Dec 2017 10:55
Publisher:Elsevier
ISSN:0001-8708
Publisher DOI:https://doi.org/10.1016/j.aim.2014.03.029

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