Abelian categories arising from cluster-tilting subcategories II: quotient functors

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.

arXiv comment25 pages

References in corpus (2)

• Quotients of exact categories by cluster tilting subcategories as module categories
• Abelian quotients of triangulated categories

Cited by in corpus (2)

• Localization of triangulated categories with respect to extension-closed subcategories
• Continuous Quivers of Type A (IV) Continuous Mutation and Geometric Models of $\mathbf{E}$-clusters