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COHOMOLOGICAL MACKEY 2-FUNCTORS

Part of: Homotopy theory Connections with homological algebra and category theory Special categories

Published online by Cambridge University Press:  18 August 2022

Paul Balmer Open the ORCID record for Paul Balmer [Opens in a new window]  and
Ivo Dell’Ambrogio
Paul Balmer*
Affiliation:
UCLA Mathematics Department, Los Angeles, CA 90095-1555, USA
Ivo Dell’Ambrogio
Affiliation:
Univ. Lille, CNRS, UMR 8524—Laboratoire Paul Painlevé, F-59000 Lille, France (ivo.dell-ambrogio@univ-lille.fr)
*
balmer@math.ucla.edu
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Abstract

We show that the bicategory of finite groupoids and right-free permutation bimodules is a quotient of the bicategory of Mackey 2-motives introduced in [2], obtained by modding out the so-called cohomological relations. This categorifies Yoshida’s theorem for ordinary cohomological Mackey functors and provides a direct connection between Mackey 2-motives and the usual blocks of representation theory.

Keywords

Mackey functorsMackey 2-functorsMackey 2-motivesYoshidaBisetsPermutation modulesDecategorification

MSC classification

Primary: 20J05: Homological methods in group theory
Secondary: 18B40: Groupoids, semigroupoids, semigroups, groups (viewed as categories) 55P91: Equivariant homotopy theory
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 23 , Issue 1 , January 2024 , pp. 279 - 309
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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Footnotes

First-named author partially supported by NSF grant DMS-1901696.

Second-named author partially supported by Project ANR ChroK (ANR-16-CE40-0003) and Labex CEMPI (ANR-11-LABX-0007-01).

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