منابع مشابه
Deformation Theory of Abelian Categories
In this paper we develop the basic infinitesimal deformation theory of abelian categories. This theory yields a natural generalization of the wellknown deformation theory of algebras developed by Gerstenhaber. As part of our deformation theory we define a notion of flatness for abelian categories. We show that various basic properties are preserved under flat deformations and we construct sever...
متن کاملSemi-abelian categories, torsion theories and factorisation systems
Semi-abelian categories [5] provide a suitable axiomatic context to study, among other things, the (co)homology of non-abelian algebraic structures (such as groups, compact groups, crossed modules, commutative rings, and Lie algebras), torsion and radical theories, and commutator theory. In this talk a brief introduction to some elementary properties of these categories will be given, before fo...
متن کاملRelative commutator theory in semi-abelian categories
Based on the concept of double central extension from categorical Galois theory, we study a notion of commutator which is defined relative to a Birkhoff subcategory B of a semi-abelian category A. This commutator characterises Janelidze and Kelly’s B-central extensions; when the subcategoryB is determined by the abelian objects inA, it coincides with Huq’s commutator; and when the category A is...
متن کاملGorenstein projective objects in Abelian categories
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 respect to $mathcal {X}$ and $mathcal{Y}_{mathcal{X}}$, respectively, where $mathcal{Y}_{mathcal{X}}$=${ Yin Ch(mathcal {A})| Y$ is acyclic and $Z_{n}Yinmathcal{X}}$. We point out that under certain hypotheses, these two G...
متن کاملObstruction Theory for Objects in Abelian and Derived Categories
In this paper we develop the obstruction theory for lifting complexes, up to quasi-isomorphism, to derived categories of flat nilpotent deformations of abelian categories. As a particular case we also obtain the corresponding obstruction theory for lifting of objects in terms of Yoneda Extgroups. In appendix we prove the existence of miniversal derived deformations of complexes.
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: Transactions of the American Mathematical Society
سال: 1966
ISSN: 0002-9947
DOI: 10.2307/1994341