Classifying Substructures of Extriangulated Categories via Serre Subcategories
نویسندگان
چکیده
We give a classification of substructures (= closed subbifunctors) given skeletally small extriangulated category by using the defects, in similar way to author’s exact structures additive category. More precisely, for an category, possible are bijection with Serre subcategories abelian consisting defects conflations. As byproduct, we prove that poset on it is isomorphic some
منابع مشابه
Classifying Serre subcategories of finitely presented modules
Given a commutative coherent ring R, a bijective correspondence between the thick subcategories of perfect complexes Dper(R) and the Serre subcategories of finitely presented modules is established. To construct this correspondence, properties of the Ziegler and Zariski topologies on the set of isomorphism classes of indecomposable injective modules are used in an essential way.
متن کاملClasses of Modules Related to Serre Subcategories
Let R be an associative ring with non-zero identity. For a Serre subcategory C of the category R-mod of left R-modules, we consider the class AC of all modules that do not belong to C, but all of their proper submodules belong to C. Alongside of basic properties of such associated classes of modules, we will prove that every uniform module of AC has a local endomorphism ring. Moreover, if R is ...
متن کاملClassifying Subcategories of Modules
Let R be the quotient of a regular coherent commutative ring by a finitely generated ideal. In this paper, we classify all abelian subcategories of finitely presented R-modules that are closed under extensions. We also classify abelian subcategories of arbitrary R-modules that are closed under extensions and coproducts, when R is commutative and Noetherian. The method relies on comparison with ...
متن کاملReconstructing Projective Schemes from Serre Subcategories
Given a positively graded commutative coherent ring A = ⊕j>0Aj , finitely generated as an A0-algebra, a bijection between the tensor Serre subcategories of qgrA and the set of all subsets Y ⊆ Proj A of the form Y =
متن کاملExtension functors of generalized local cohomology modules and Serre subcategories
In this paper we present several results concerning the cofiniteness of generalized local cohomology modules.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Applied Categorical Structures
سال: 2021
ISSN: ['1572-9095', '0927-2852']
DOI: https://doi.org/10.1007/s10485-021-09642-0