Tilting objects in triangulated categories
Y Hu, H Yao, X Fu - Communications in Algebra, 2020 - Taylor & Francis
Based on Beligiannis's theory in [Beligiannis, A.(2000). Relative homological algebra and
purity in triangulated categories. J. Algebra 227 (1): 268–361], we introduce and study E …
purity in triangulated categories. J. Algebra 227 (1): 268–361], we introduce and study E …
Tilting subcategories in extriangulated categories
B Zhu, X Zhuang - Frontiers of Mathematics in China, 2020 - Springer
Extriangulated category was introduced by H. Nakaoka and Y. Palu to give a unification of
properties in exact categories and triangulated categories. A notion of tilting (resp., cotilting) …
properties in exact categories and triangulated categories. A notion of tilting (resp., cotilting) …
[HTML][HTML] Hearts of twin cotorsion pairs on extriangulated categories
Y Liu, H Nakaoka - Journal of Algebra, 2019 - Elsevier
In this article, we study the heart of a cotorsion pairs on an exact category and a triangulated
category in a unified method, by means of the notion of an extriangulated category. We …
category in a unified method, by means of the notion of an extriangulated category. We …
Proper classes and Gorensteinness in extriangulated categories
J Hu, D Zhang, P Zhou - Journal of algebra, 2020 - Elsevier
Extriangulated categories were introduced by Nakaoka and Palu as a simultaneous
generalization of exact categories and triangulated categories. A notion of proper class in an …
generalization of exact categories and triangulated categories. A notion of proper class in an …
Left Frobenius pairs, cotorsion pairs and weak Auslander-Buchweitz contexts in triangulated categories
X Ma, T Zhao, Z Huang - Algebra Colloquium, 2024 - World Scientific
Let T be a triangulated category with a proper class ξ of triangles. We introduce the notions
of left Frobenius pairs, left (n-) cotorsion pairs and left (weak) Auslander-Buchweitz contexts …
of left Frobenius pairs, left (n-) cotorsion pairs and left (weak) Auslander-Buchweitz contexts …
A bijection between tilting subcategories and cotorsion pairs in extriangulated categories
Z Zhu, J Wei - arXiv preprint arXiv:2403.03546, 2024 - arxiv.org
Let $\mathscr {C} $ be an extriangulated category with enough projectives and injectives.
We give a new definition of tilting subcategories of $\mathscr {C} $ and prove it coincides …
We give a new definition of tilting subcategories of $\mathscr {C} $ and prove it coincides …
Right triangulated categories with right semi-equivalences
I Assem, A Beligiannis… - CMS Conference …, 1998 - books.google.com
We show that a right triangulated category is best behaved when its shift satisfies conditions
making it what we call a right semi-equivalence. We consider right triangulated categories …
making it what we call a right semi-equivalence. We consider right triangulated categories …
General heart construction on a triangulated category (II): Associated homological functor
N Abe, H Nakaoka - Applied Categorical Structures, 2012 - Springer
In the preceding part (I) of this paper, we showed that for any torsion pair (ie, t-structure
without the shift-closedness) in a triangulated category, there is an associated abelian …
without the shift-closedness) in a triangulated category, there is an associated abelian …
Cotorsion pairs in a recollement of triangulated categories
J Chen - Communications in Algebra, 2013 - Taylor & Francis
In the present article, we study the relationship of cotorsion pairs among three triangulated
categories in a recollement. We show that if a triangulated category 𝒟 admits a recollement …
categories in a recollement. We show that if a triangulated category 𝒟 admits a recollement …
Construct ideal cotorsion pairs by recollement of triangulated categories
Q Wang, H Zhu - arXiv preprint arXiv:2406.00417, 2024 - arxiv.org
Let $(\mathcal {T}',\mathcal {T},\mathcal {T}'') $ be a recollement of triangulated categories.
Two complete ideal cotorsion pairs in $\mathcal {T}'$ and $\mathcal {T}''$ can be induced by …
Two complete ideal cotorsion pairs in $\mathcal {T}'$ and $\mathcal {T}''$ can be induced by …