A characterisation of higher torsion classes
Résumé
Let A be an abelian length category containing a d-cluster tilting subcategory M. We prove that a subcategory of M is a d-torsion class if and only if it is closed under d-extensions and d-quotients. This generalises an important result for classical torsion classes. As an application, we prove that the d-torsion classes in M form a complete lattice. Moreover, we use the characterisation to classify the d-torsion classes associated to higher Auslander algebras of type A, and give an algorithm to compute them explicitly. The classification is furthermore extended to the setup of higher Nakayama algebras.
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