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Abelian categories arising from cluster-tilting subcategories II: quotient functors (1809.06597v1)
Published 18 Sep 2018 in math.RT and math.CT
Abstract: In this paper, we consider a kind of ideal quotient of an extriangulated category such that the ideal is the kernel of a functor from this extriangulated category to an abelian category. We study a condition when the functor is dense and full, in another word, the ideal quotient becomes abelian. Moreover, a new equivalent characterization of cluster-tilting subcategories is given by applying homological methods according to this functor. As an application, we show that in a connected 2-Calabi-Yau triangulated category B, a functorially finite, extension closed subcategory T of B is cluster tilting if and only if B/T is an abelian category.