Fibered Biset Functors

TL;DR

This paper develops the theory of fibered biset functors, extending classical biset functors to a framework that captures operations induced by monomial bimodules, and classifies their simple objects.

Contribution

It introduces fibered biset functors and provides a classification of their simple objects, expanding the algebraic framework for representation-theoretic operations.

Findings

Classification of simple fibered biset functors

Extension of biset functor theory to fibered case

Framework for operations induced by monomial bimodules

Abstract

The theory of biset functors, introduced by Serge Bouc, gives a unified treatment of operations in representation theory that are induced by permutation bimodules. In this paper, by considering fibered bisets, we introduce and describe the basic theory of fibered biset functors which is a natural framework for operations induced by monomial bimodules. The main result of this paper is the classification of simple fibered biset functors.