Higher Auslander’s Formula

Abstract Let $\mathcal{M}$ be a small $n$-abelian category. We show that the category of finitely presented functors ${\operatorname{mod}}$-$\mathcal{M}$ modulo subcategory effaceable ${\operatorname{mod}}_0$-$\mathcal{M}$ has an $n$-cluster tilting subcategory, which is equivalent to $\mathcal{M}$. This gives higher-dimensional version Auslander’s formula.