[HTML][HTML] Totally acyclic complexes

S Estrada, X Fu, A Iacob - Journal of Algebra, 2017 - Elsevier
It is known that over an Iwanaga–Gorenstein ring the Gorenstein injective (Gorenstein
projective, Gorenstein flat) modules are simply the cycles of acyclic complexes of injective …

Special precovering classes in comma categories

J Hu, H Zhu - Science China Mathematics, 2022 - Springer
Let T be a right exact functor from an abelian category ℬ into another abelian category A.
Then there exists a functor p from the product category A× ℬ to the comma category ((T↓ …

Balanced pairs, cotorsion triplets and quiver representations

S Estrada, MA Perez, H Zhu - Proceedings of the Edinburgh …, 2020 - cambridge.org
Balanced pairs appear naturally in the realm of relative homological algebra associated with
the balance of right-derived functors of the Hom functor. Cotorsion triplets are a natural …

Maximum deconstructibility in module categories

S Cox - Journal of Pure and Applied Algebra, 2022 - Elsevier
We prove that Vopěnka's Principle implies that for every class X of modules over any ring,
the class of X-Gorenstein Projective modules (X-GP) is a precovering class. In particular, it is …

Gorenstein AC-projective complexes

J Gillespie - Journal of Homotopy and Related Structures, 2018 - Springer
Let R be any ring with identity and Ch (R) C h (R) the category of chain complexes of (left) R-
modules. We show that the Gorenstein AC-projective chain complexes of 1 are the cofibrant …

Approximation Theory and Elementary Submodels

S Cox - arXiv preprint arXiv:2405.19634, 2024 - arxiv.org
\emph {Approximation Theory} uses nicely-behaved subcategories to understand entire
categories, just as projective modules are used to approximate arbitrary modules in classical …

[图书][B] Gorenstein homological algebra

A Iacob - 2018 - taylorfrancis.com
Gorenstein homological algebra is an important area of mathematics, with applications in
commutative and noncommutative algebra, model category theory, representation theory …

A Zariski-local notion of F-total acyclicity for complexes of sheaves

LW Christensen, S Estrada, A Iacob - Quaestiones Mathematicae, 2017 - Taylor & Francis
We study a notion of total acyclicity for complexes of flat sheaves over a scheme. It is Zariski-
local—ie it can be verified on any open affine covering of the scheme—and for sheaves over …

Abelian model structures on categories of quiver representations

G Dalezios - Journal of Algebra and Its Applications, 2020 - World Scientific
Let ℳ be an abelian model category (in the sense of Hovey). For a large class of quivers, we
describe associated abelian model structures on categories of quiver representations with …

Ideal balanced pairs

J Asadollahi, S Hemat, R Vahed - Journal of Algebra and Its …, 2021 - World Scientific
In this paper, ideal balanced pairs in an abelian category will be introduced and studied. It is
proved that every ideal balanced pair gives rise to a triangle equivalence of relative derived …