# The generalized Auslander-Reiten duality on a module category

## TL;DR

This paper characterizes a generalized form of Auslander-Reiten duality within certain module categories, including categories like FI and VI, expanding the understanding of dualities in representation theory.

## Contribution

It introduces a characterization of the generalized Auslander-Reiten duality for finitely presented modules over specific Hom-finite categories, including new examples such as FI and VI.

## Key findings

- Provides a new duality framework for module categories
- Includes examples like FI and VI categories
- Enhances understanding of dualities in representation theory

## Abstract

We characterize the generalized Auslander--Reiten duality on the category of finitely presented modules over some certain Hom-finite category. Examples include the category FI of finite sets with injections, and the one VI of finite dimensional vector spaces with linear injections over a finite field.