Mackey formula for bisets over groupoids

TL;DR

This paper extends the Mackey formula, a fundamental result in representation theory, to the context of groupoids, involving bisets, orbit sets, and tensor products over groupoids.

Contribution

It introduces a Mackey formula for groupoids, generalizing the classical group case to a broader algebraic structure.

Findings

Established the Mackey formula for groupoids

Extended biset and tensor product concepts to groupoids

Provided a framework for subgroupoid cosets and their interactions

Abstract

In this paper we establish the Mackey formula for groupoids, extending the well known formula in abstract groups context. This formula involves the notion of groupoid-biset, its orbit set and the tensor product over groupoids, as well as cosets by subgroupoids.