Complete Cohomology for Extriangulated Categories
نویسندگان
چکیده
Let [Formula: see text] be an extriangulated category with a proper class of text]-triangles. We study complete cohomology objects in by applying text]-projective resolutions and text]-injective coresolutions constructed text]. Vanishing detects finite dimension dimension. As consequence, we obtain some criteria for the validity Wakamatsu tilting conjecture give necessary sufficient condition virtually Gorenstein algebra to Gorenstein. Moreover, general technique computing text]-[Formula: text]projective application, relations between are given.
منابع مشابه
Cohomology in Tensored Categories
Both [Mac Lane 1965, Beck 1967] have recently defined cohomology theories for algebras in abstract categorial setting. Mac Lane’s theory is an abstract formaization of the (normalised) bar construction (see [Mac Lane 1963, p. 144] for example). Since, however, his proof of the normalization theorem (p. 236) remains perfectly valid, the normalized bar construction can be replaced by the un-norma...
متن کاملCohomology and Tensor Categories
In this research announcement we propose the notion of a supercategory as an alternative approach to supermathematics. We show that this setting is rich to carry out many of the basic constructions of supermathematics. We also prove generalizations of a number of results in equivariant cohomology, including the Chern-Weil theorem for an arbitrary rigid Lie algebra object. For a quadratic Lie al...
متن کاملCohomology Theory in 2-categories
Recently, symmetric categorical groups are used for the study of the Brauer groups of symmetric monoidal categories. As a part of these efforts, some algebraic structures of the 2-category of symmetric categorical groups SCG are being investigated. In this paper, we consider a 2-categorical analogue of an abelian category, in such a way that it contains SCG as an example. As a main theorem, we ...
متن کاملMonoidal Categories, 2-traces, and Cyclic Cohomology
In this paper we show that to a unital associative algebra object (resp. co-unital coassociative co-algebra object) of any abelian monoidal category (C,⊗) endowed with a symmetric 2-trace, i.e. an F ∈ Fun(C,Vec) satisfying some natural trace-like conditions, one can attach a cyclic (resp. cocyclic) module, and therefore speak of the (co)cyclic homology of the (co)algebra “with coefficients in F...
متن کاملLECTURES ON n-CATEGORIES AND COHOMOLOGY
1. The Basic Principle of Galois Theory 3 1.1. Galois theory and the Erlangen program 3 1.2. The fundamental group 4 1.3. The fundamental groupoid 4 1.4. Eilenberg–Mac Lane Spaces 5 1.5. Klein’s favorite example 6 1.6. Grothendieck’s dream 8 2. The Power of Negative Thinking 10 2.1. Extending the periodic table 10 2.2. The categorical approach 13 2.3. Homotopy n-types 14 2.4. Stuff, structure, ...
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: Algebra Colloquium
سال: 2021
ISSN: ['0219-1733', '1005-3867']
DOI: https://doi.org/10.1142/s1005386721000547