Modules with injective cohomology, and local duality for a finite group.
Monads and cohomology modules of rank 2 vector bundles
Monotone-light factorization for Kan fibrations of simplicial sets with respect to groupoids.
Moore categories.
More about homological properties of precrossed modules.
More about the (co)homology of groups and associative algebras.
More on injectivity in locally presentable categories.
Morita Equivalences of Functor Categories and Decompositions of Functors Defined on a Category Associated to Algebras with One-Side Units
Conditions which imply Morita equivalences of functor categories are described. As an application a Dold-Kan type theorem for functors defined on a category associated to associative algebras with one-side units is proved.
Motivically functorial coniveau spectral sequences; direct summands of cohomology of function fields.
-strongly Gorenstein graded modules
Let be a graded ring and an integer. We introduce and study -strongly Gorenstein gr-projective, gr-injective and gr-flat modules. Some examples are given to show that -strongly Gorenstein gr-injective (gr-projective, gr-flat, respectively) modules need not be -strongly Gorenstein gr-injective (gr-projective, gr-flat, respectively) modules whenever . Many properties of the -strongly Gorenstein gr-injective and gr-flat modules are discussed, some known results are generalized. Then we investigate...
Non-abelian cohomology of associative algebras. The -term exact sequence
Non-abelian cohomology of groups.
Non-abelian cohomology via parity quasi-complexes.
Non-abelian cohomology with coefficients in crossed bimodules.
Non-abelian tensor and exterior products modulo and universal -central relative extension of Lie algebra.
Non-abelian tensor product of Lie algebras and its derived functors.
Non-commutative differential geometry
Noncommutative numerical motives, Tannakian structures, and motivic Galois groups
In this article we further the study of noncommutative numerical motives, initiated in [30, 31]. By exploring the change-of-coefficients mechanism, we start by improving some of the main results of [30]. Then, making use of the notion of Schur-finiteness, we prove that the category NNum of noncommutative numerical motives is (neutral) super-Tannakian. As in the commutative world, NNum is not Tannakian. In order to solve this problem we promote periodic cyclic homology to a well-defined symmetric...
Nondegenerate cohomology pairing for transitive Lie algebroids, characterization
The Evens-Lu-Weinstein representation (Q A, D) for a Lie algebroid A on a manifold M is studied in the transitive case. To consider at the same time non-oriented manifolds as well, this representation is slightly modified to (Q Aor, Dor) by tensoring by orientation flat line bundle, Q Aor=QA⊗or (M) and D or=D⊗∂Aor. It is shown that the induced cohomology pairing is nondegenerate and that the representation (Q Aor, Dor) is the unique (up to isomorphy) line representation for which the top group of...
Normal functors and strong protomodularity.