Bisets as categories, and tensor product of induced bimodules

TL;DR

This paper explores the categorical perspective of bisets to provide a simplified proof of a Mackey-like formula for the tensor product of induced bimodules, enhancing understanding of their algebraic structure.

Contribution

It introduces a categorical framework for bisets to derive a straightforward proof of a key tensor product formula in bimodule theory.

Findings

Categorical interpretation of bisets simplifies tensor product proofs.

Provides a new proof of a Mackey-like formula for induced bimodules.

Enhances algebraic understanding of bimodule tensor products.

Abstract

Bisets can be considered as categories. This note uses this point of view to give a simple proof of a Mackey-like formula expressing the tensor product of two induced bimodules.