Axiomatic representation theory of finite groups by way of groupoids

DOI10.1017/9781108942874.004arXiv1910.03369MaRDI QIDQ6326763

Publication date: 8 October 2019

Abstract: We survey several notions of Mackey functors and biset functors found in the literature and prove some old and new theorems comparing them. While little here will surprise the experts, we draw a conceptual and unified picture by making systematic use of finite groupoids. This provides a road map for the various approaches to the axiomatic representation theory of finite groups, as well as some details which are hard to find in writing.

Mathematics Subject Classification ID

Representation theory of groups (20C99) Groupoids (i.e. small categories in which all morphisms are isomorphisms) (20L05) 2-categories, bicategories, double categories (18N10)

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