Invariants of a Free Linear Category and Representation Type

TL;DR

This paper proves that taking invariants under a finite group action preserves the freeness and representation type of a free linear category, providing insights into the structure and classification of such categories.

Contribution

It demonstrates that the subcategory of invariants remains free and retains the same representation type under finite group actions, extending understanding of invariants in linear categories.

Findings

Invariants form a free subcategory under finite group actions.

Representation type is preserved in invariant subcategories.

Provides structural results for categories with group symmetries.

Abstract

We consider an homogeneous action of a finite group on a free linear category over a field in order to prove that the subcategory of invariants is still free. Moreover we show that the representation type is preserved when considering invariants.