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 the subcategory of effaceable functors ${\operatorname{mod}}_0$-$\mathcal{M}$ has an $n$-cluster tilting subcategory, which is equivalent to $\mathcal{M}$. This gives a higher-dimensional version of Auslander’s formula.