  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.
