# Local Representation Theory of Transporter Categories

## TL;DR

This paper extends the p-modular representation theory from finite groups to finite transporter categories using transporter category algebras and Kan extensions, generalizing key local representation theory concepts.

## Contribution

It introduces a framework for the local representation theory of transporter categories, generalizing classical finite group results with new algebraic tools.

## Key findings

- Generalization of local representation theory to transporter categories
- Development of modules over transporter category algebras
- Use of Kan extensions to relate representations

## Abstract

We attempt to generalize the $p$-modular representation theory of finite groups to finite transporter categories, which are regarded as generalized groups. We shall carry on our tasks through modules of transporter category algebras, a type of Gorenstein skew group algebras. The Kan extensions, upgrading the induction and co-induction, are our main tools to establish connections between representations of a transporter category and of its transporter subcategories. Some important constructions and theorems in local representation theory of finite groups are generalized.