[HTML][HTML] Coderived and contraderived categories of locally presentable abelian DG-categories
L Positselski, J Št'ovíček - Mathematische Zeitschrift, 2024 - Springer
The concept of an abelian DG-category, introduced by the first-named author in Positselski
(Exact DG-categories and fully faithful triangulated inclusion functors. arXiv: 2110.08237 …
(Exact DG-categories and fully faithful triangulated inclusion functors. arXiv: 2110.08237 …
Applications of exact structures in abelian categories
J Wang, Z Huang - arXiv preprint arXiv:1510.07098, 2015 - arxiv.org
In an abelian category $\mathscr {A} $ with small ${\rm Ext} $ groups, we show that there
exists a one-to-one correspondence between any two of the following: balanced pairs …
exists a one-to-one correspondence between any two of the following: balanced pairs …
0-Auslander correspondence
X Chen - arXiv preprint arXiv:2306.15958, 2023 - arxiv.org
arXiv:2306.15958v1 [math.RT] 28 Jun 2023 Page 1 0-AUSLANDER CORRESPONDENCE
XIAOFA CHEN Abstract. We prove an analogue of Auslander correspondence for exact dg …
XIAOFA CHEN Abstract. We prove an analogue of Auslander correspondence for exact dg …
Idempotent completion of certain -exangulated categories
J He, J He, P Zhou - arXiv preprint arXiv:2207.01232, 2022 - arxiv.org
It was shown recently that an $ n $-extension closed subcategory $\mathscr A $ of a Krull-
Schmidt $(n+ 2) $-angulated category has a natural structure of an $ n $-exangulated …
Schmidt $(n+ 2) $-angulated category has a natural structure of an $ n $-exangulated …
[PDF][PDF] Stratified exact categories and highest weight representations
MJ Dyer - preprint - nd.edu
We define stratified exact categories, which are a class of exact categories abstracting very
general features of the category of modules with a Verma flag in a highest weight category …
general features of the category of modules with a Verma flag in a highest weight category …
Heart of irreducible morphisms of bounded complexes
H Giraldo, E Marcos - Communications in Algebra, 2016 - Taylor & Francis
In Giraldo and Merklen studied irreducible morphisms in the categories 𝒞 (𝒜) and D−(Λ),
where 𝒞 (𝒜) is the category of complexes over an abelian Krull–Schmidt category 𝒜 and …
where 𝒞 (𝒜) is the category of complexes over an abelian Krull–Schmidt category 𝒜 and …
Universal co-extensions of torsion abelian groups
A Argudín-Monroy, CE Parra - Journal of Algebra, 2024 - Elsevier
Abstract In [16], a theory of universal extensions in abelian categories is developed; in
particular, the notion of Ext 1-universal object is presented. In the present paper, we show …
particular, the notion of Ext 1-universal object is presented. In the present paper, we show …
The Yoneda Ext and arbitrary coproducts in abelian categories
A Argudin-Monroy - Glasgow Mathematical Journal, 2022 - cambridge.org
There are well-known identities involving the Ext bifunctor, coproducts, and products in AB4
abelian categories with enough projectives. Namely, for every such category\[\mathcal {A}\] …
abelian categories with enough projectives. Namely, for every such category\[\mathcal {A}\] …
[PDF][PDF] Abelian groupoids and non-pointed additive categories
D Bourn - Theory and Applications of Categories, 2008 - epe.lac-bac.gc.ca
We show that, in any Mal'tsev (and a fortiori protomodular) category E, not only the fibre
GrdXE of internal groupoids above the object X is a naturally Mal'tsev category, but …
GrdXE of internal groupoids above the object X is a naturally Mal'tsev category, but …