Higher Auslander's formula

TL;DR

This paper extends Auslander's formula to higher dimensions by showing that for a small n-abelian category, the quotient of finitely presented functors by effaceable functors has an n-cluster tilting subcategory equivalent to the original category.

Contribution

It introduces a higher-dimensional version of Auslander's formula connecting n-abelian categories and n-cluster tilting subcategories.

Findings

Establishes an equivalence between a quotient category and the original n-abelian category.

Identifies an n-cluster tilting subcategory within the quotient of finitely presented functors.

Provides a higher-dimensional generalization of classical Auslander's formula.

Abstract

Let $\mathcal{M}$ be a small $n$-abelian category. We show that the category of finitely presented functors $mod$-$\mathcal{M}$ modulo the subcategory of effaceable functors $mod_0$-$\mathcal{M}$ has an $n$-cluster tilting subcategory which is equivalent to $\mathcal{M}$. This gives a higher-dimensional version of Auslander's formula.