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mackey 2-functors

Journal of the Institute of Mathematics of Jussieu (1)

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COHOMOLOGICAL MACKEY 2-FUNCTORS
Part of
Paul Balmer, Ivo Dell’Ambrogio
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 23 / Issue 1 / January 2024

Published online by Cambridge University Press:

18 August 2022, pp. 279-309

Print publication:

January 2024
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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.