Heller's axioms for homotopy theory
A notion of hereditarity of a closure operator with respect to a class of monomorphisms is introduced. Let be a regular closure operator induced by a subcategory . It is shown that, if every object of is a subobject of an -object which is injective with respect to a given class of monomorphisms, then the closure operator is hereditary with respect to that class of monomorphisms.
Zhou and Zhu have shown that if is an -angulated category and is a cluster tilting subcategory of , then the quotient category is an -abelian category. We show that if has Auslander-Reiten -angles, then has Auslander-Reiten -exact sequences.