Support -tilting modules and recollements

X Ma, Z Xie, T Zhao - arXiv preprint arXiv:1801.02343, 2018 - arxiv.org
Let $(\mbox {mod}\Lambda',\mbox {mod}\Lambda,\mbox {mod}\Lambda'') $ be a recollement
of abelian categories for artin algebras $\Lambda'$, $\Lambda $ and $\Lambda''$. Under …

Components of Auslander-Reiten quivers with only preprojective modules

FU Coelho - Journal of Algebra, 1993 - Elsevier
with Only Preprojective Modules Page 1 JOURNAL OF ALGEBRA 157, 472–488 (1993)
Components of Auslander–Reiten Ouivers with Only Preprojective Modules FLÁVIO ULHOA …

Tilting pairs in extriangulated categories

T Zhao, B Zhu, X Zhuang - Proceedings of the Edinburgh …, 2021 - cambridge.org
Extriangulated categories were introduced by Nakaoka and Palu to give a unification of
properties in exact categories and extension-closed subcategories of triangulated …

Syzygy properties under recollements of derived categories

K Wu, J Wei - Journal of Algebra, 2022 - Elsevier
Abstract Let A, B and C be artin algebras such that there is a recollement of D (Mod A)
relative to D (Mod B) and D (Mod C). We compare the algebras A, B and C with respect to …

[HTML][HTML] Pullback diagrams, syzygy finite classes and Igusa–Todorov algebras

D Bravo, M Lanzilotta, O Mendoza - Journal of Pure and Applied Algebra, 2019 - Elsevier
For an abelian category A, we define the category PEx (A) of pullback diagrams of short
exact sequences in A, as a subcategory of the functor category Fun (Δ, A) for a fixed diagram …

The Bongartz's theorem on the homotopy category

Y Hu, H Yao - Bulletin of the Iranian Mathematical Society, 2019 - Springer
Let Λ Λ be an Artin algebra and M ∈ M∈ mod Λ Λ. It is well-known that the Bongartz's
Theorem plays an important role in the representation theory of Artin algebras. In this paper …

Auslander's formula and correspondence for exact categories

R Henrard, S Kvamme, AC Van Roosmalen - Advances in Mathematics, 2022 - Elsevier
The Auslander correspondence is a fundamental result in Auslander-Reiten theory. In this
paper we introduce the category mo d adm (E) of admissibly finitely presented functors and …

[图书][B] Auslander-Reiten theory via Brown representability

H Krause - 1999 - Citeseer
We develop an Auslander-Reiten theory for triangulated categories which is based on
Brown's representability theorem. In a fundamental article [3], Auslander and Reiten …

[PDF][PDF] Relative theory in subcategories

SK Mohamed - Colloq. Math, 2009 - Citeseer
We generalize the relative (co) tilting theory of Auslander-Solberg [9, 10] in the category mod
Λ of finitely generated left modules over an artin algebra Λ to certain subcategories of mod …

[图书][B] The category of good modules over a quasi-hereditary algebra has almost split sequences

CM Ringel - 1989 - pub.uni-bielefeld.de
Let A be a quasi-hereditary algebra. The aim of this paper is to show that the category of all
A-modules with good filtrations is functorially finite in A-mod, thus it has (relative) almost split …