Cohomological Mackey 2-functors

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 arXiv:1808.04902, 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.

arXiv commentA few remaining typos corrected in journal proofs. 28 pages, final version, to appear in J. Inst. Math. Jussieu

References in corpus (6)

• Stacks of group representations
• Mackey 2-functors and Mackey 2-motives
• Green equivalences in equivariant mathematics
• On the comparison of spans and bisets
• A categorification of the Cartan-Eilenberg formula
• Crossed Burnside rings and cohomological Mackey $2$-motives

Cited by in corpus (1)

• An introduction to Mackey and Green 2-functors