Higher 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 $mo{d}_0$-$\mathcal{M}$ has an $n$-cluster tilting subcategory which is equivalent to $\mathcal{M}$. This gives a higher-dimensional version of Auslander's formula.

arXiv admin note: text overlap with arXiv:2001.01254

References in corpus (2)

• Transport of structure in higher homological algebra
• Projectively generated $d$-abelian categories are $d$-cluster tilting

Cited by in corpus (4)

• Higher Auslander correspondence for exact categories
• On higher torsion classes
• A characterisation of higher torsion classes
• Gabriel-Quillen embedding for $n$-exact categories