Silting reduction in extriangulated categories
Y Liu, P Zhou, Y Zhou, B Zhu - arXiv preprint arXiv:2108.07964, 2021 - arxiv.org
Presilting and silting subcategories in extriangulated categories were introduced by Adachi
and Tsukamoto recently. In this paper, we prove that the Gabriel-Zisman localization …
and Tsukamoto recently. In this paper, we prove that the Gabriel-Zisman localization …
One-sided Frobenius pairs in extriangulated categories
L Tan, Y Gao, Q Chen - Communications in Algebra, 2022 - Taylor & Francis
Let C be an extriangulated category with a proper class ξ of E-triangles. We introduce the
notions of left Frobenius pairs, left (n-) cotorsion pairs and left (weak) Auslander-Buchweitz …
notions of left Frobenius pairs, left (n-) cotorsion pairs and left (weak) Auslander-Buchweitz …
Proper resolutions and Gorensteinness in extriangulated categories
J Hu, D Zhang, P Zhou - Frontiers of Mathematics in China, 2021 - Springer
Abstract Let (C, E, s C, E, s) be an extriangulated category with a proper class ξ of E E-
triangles, and WW an additive full subcategory of (C, E, s C, E, s). We provide a method for …
triangles, and WW an additive full subcategory of (C, E, s C, E, s). We provide a method for …
Model structures and recollements induced by duality pairs
W Chen, L Li, Y Rao - arXiv preprint arXiv:2108.00140, 2021 - arxiv.org
We give some equivalent characterizations of $\mathcal {GP} $, the class of Gorenstein
$(\mathcal {L},\mathcal {A}) $-projective modules, and construct some model structures …
$(\mathcal {L},\mathcal {A}) $-projective modules, and construct some model structures …
Frobenius templicial modules and the dg-nerve
W Lowen, A Mertens - arXiv preprint arXiv:2005.04778, 2020 - arxiv.org
Templicial objects were put forth in arXiv: 2302.02484 v2 to set up a suitable simplicial
framework for enriched quasi-categories. Following Leinster, these objects feature certain …
framework for enriched quasi-categories. Following Leinster, these objects feature certain …
Stable functors of derived equivalences and Gorenstein projective modules
From certain triangle functors, called nonnegative functors, between the bounded derived
categories of abelian categories with enough projective objects, we introduce their stable …
categories of abelian categories with enough projective objects, we introduce their stable …
New model structures and projective (injective) cotorsion pairs
A Xu - Journal of Algebra and Its Applications, 2023 - World Scientific
Let 𝒟 be either the category of R-modules or the category of chain complexes of R-modules
and ℳ a cofibrantly generated hereditary abelian model structure on 𝒟. First, we get a new …
and ℳ a cofibrantly generated hereditary abelian model structure on 𝒟. First, we get a new …
[PDF][PDF] Gorenstein projective objects in Abelian categories
H Cheng, X Zhu - Bulletin of the Iranian Mathematical Society, 2013 - bims.iranjournals.ir
Let $ mathcal {A} $ be an abelian category with enough projective objects and $ mathcal {X}
$ be a full subcategory of $ mathcal {A} $. We define Gorenstein projective objects with …
$ be a full subcategory of $ mathcal {A} $. We define Gorenstein projective objects with …
Galois G-covering of quotients of linear categories
Y Hu, P Zhou - Journal of Pure and Applied Algebra, 2023 - Elsevier
In this paper, we introduce the notion of G-liftable ideals, which extends the liftable ideas
defined by Assem and Le Meur. We characterize the G-liftable ideals and construct the …
defined by Assem and Le Meur. We characterize the G-liftable ideals and construct the …
The stable monomorphism category of a Frobenius category
XW Chen - arXiv preprint arXiv:0911.1987, 2009 - arxiv.org
For a Frobenius abelian category $\mathcal {A} $, we show that the category ${\rm
Mon}(\mathcal {A}) $ of monomorphisms in $\mathcal {A} $ is a Frobenius exact category; …
Mon}(\mathcal {A}) $ of monomorphisms in $\mathcal {A} $ is a Frobenius exact category; …