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.

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

References in corpus (3)

• 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