31 citations · 103 across the 27 of their papers we have counts for
22 papers · 1 filter
Quasi-abelian quotients in extriangulated categories
Yu Liu, Yu-Zhe Liu, Panyue Zhou
Let be an extriangulated category. Motivated by the theory of hereditary algebras, we introduce the notion of a hereditary-type subcategor…
Largest exact structures and almost split sequences on hearts of twin cotorsion pairs
Yu Liu, Wuzhong Yang, Panyue Zhou
Hearts of cotorsion pairs on extriangulated categories are abelian categories. On the other hand, hearts of twin cotorsion pairs are not always abelian. They were shown to be semi-…
Hearts of twin cotorsion pairs revisited: integral and abelian hearts
Yu Liu, Panyue Zhou
Hearts of twin cotorsion pairs are shown to be quasi-abelian. But they are not always integral. In this article, we provide a sufficient and necessary condition for the hearts of t…
Extriangulated ideal quotients and Gabriel-Zisman localizations
Yu Liu, Panyue Zhou
Let be an extriangulated category and be an extension closed subcategory of . In this article, we prove that the Gab…
Gluing n-tilting and n-cotilting subcategories
Yu Liu, Panyue Zhou
Recently, Wang, Wei and Zhang define the recollement of extriangulated categories, which is a generalization of both recollement of abelian categories and recollement of triangulat…
Silting reduction in extriangulated categories
Yu Liu, Panyue Zhou, Yu Zhou +1
Presilting and silting subcategories in extriangulated categories were introduced by Adachi and Tsukamoto recently. In this paper, we prove that the Gabriel-Zisman localization $\m…
Hereditary cotorsion pairs on extriangulated subcategories
Yu Liu, Panyue Zhou
Let be an extriangulated category with enough projectives and enough injectives. We define a proper -term subcategory on , which is an extr…
-tilting theory in abelian categories
Yu Liu, Panyue Zhou
Let be a Hom-finite abelian category with enough projectives. In this note, we show that any covariantly finite -rigid subcategory is contained in a support -til…
Relative rigid subcategories and -tilting theory
Yu Liu, Panyue Zhou
Let be an extriangulated category with enough projectives and enough injectives , and let be a contravariantly finite rigid subca…
From -exangulated categories to -abelian categories
Yu Liu, Panyue Zhou
Herschend-Liu-Nakaoka introduced the notion of -exangulated categories. It is not only a higher dimensional analogue of extriangulated categories defined by Nakaoka-Palu, but al…
On the relation between relative rigid and support tilting
Yu Liu, Panyue Zhou
Let B be an extriangulated category with enough projectives and enough injectives. Let C be a fully rigid subcategory of B which admits a twin cotorsion pair ((C,K),(K,D)). The quo…
Frobenius -exangulated categories
Yu Liu, Panyue Zhou
Herschend-Liu-Nakaoka introduced the notion of -exangulated categories as higher dimensional analogues of extriangulated categories defined by Nakaoka-Palu. The class of -exa…
Gorenstein dimension of abelian categories
Yu Liu, Panyue Zhou
Let C be triangulated category and X a cluster tilting subcategory of C. Koenig and Zhu showed that the quotient category C/X is Gorenstein of Gorenstein dimension at most one. The…
Abelian quotients associated with fully rigid subcategories
Yu Liu
In this article, we study the Gorenstein property of abelian quotient categories induced by fully rigid subcategories on an exact category B. We also study when d-cluster tilting s…
Abelian categories arising from cluster-tilting subcategories II: quotient functors
Yu Liu, Panyue Zhou
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 cat…
Abelian categories arising from cluster tilting subcategories
Yu Liu, Panyue Zhou
For a triangulated category T, if C is a cluster-tilting subcategory of T, then the quotient category T\C is an abelian category. Under certain conditions, the converse also holds.…
Localizations of the hearts of cotorsion pairs associated with mutations
Yu Liu
In this article, we study localizations of hearts of cotorsion pairs (U,V) where U is rigid on an extriangulated category B. The hearts of such cotorsion pairs are equivalent to th…
Hearts of cotorsion pairs are functor categories over cohearts
Yu Liu
We study hearts of cotorsion pairs in triangulated and exact categories.We give a sufficient and necessary condition when the hearts have enough projectives. We also show in such c…
Half exact functors associated with cotorsion pairs on exact categories
Yu Liu
In the previous article "Hearts of twin cotorsion pairs on exact categories", we introduced the notion of the heart for any cotorsion pair on an exact category with enough projecti…
Hearts of twin cotorsion pairs on exact categories
Yu Liu
In the papers of Nakaoka, he introduced the notion of hearts of (twin) cotorsion pairs on triangulated categories and showed that they have structures of (semi-) abelian categories…
Quotients of exact categories by cluster tilting subcategories as module categories
Laurent Demonet, Yu Liu
We prove that some subquotient categories of exact categories are abelian. This generalizes a result by Koenig-Zhu in the case of (algebraic) triangulated categories. As a particul…
Triangulated quotient categories
Yu Liu, Bin Zhu
A notion of mutation of subcategories in a right triangulated category is defined in this paper. When (Z,Z) is a D-mutation pair in a right triangulated category C, the quotient ca…