We define A∞-bimodules similarly to Tradler and show that this notion is equivalent to an A∞-functor with two arguments which takes values in the differential graded category of complexes of k-modules, where k is a ground commutative ring. Serre A∞-functors are defined via A∞-bimodules likewise Kontsevich and Soibelman. We prove that a unital closed under shifts A∞-category A over a field k adm...

We define A∞-bimodules similarly to Tradler and show that this notion is equivalent to an A∞-functor with two arguments which takes values in the differential graded category of complexes of k-modules, where k is a ground commutative ring. Serre A∞-functors are defined via A∞-bimodules likewise Kontsevich and Soibelman. We prove that a unital closed under shifts A∞-category A over a field k adm...

We develop Morita theory for finitary additive 2-representations of finitary 2-categories. As an application we describe Morita equivalence classes for 2-categories of projective functors associated to finite dimensional algebras and for 2-categories of Soergel bimodules.

For a vertex operator algebra V , the regular representations are related to the An(V )-algebras and their bimodules, and induced V -modules from An(V )-modules are defined and studied in terms of the regular representations.

There are remarkable relations between the graded homological dimensions and the ordinary homological dimensions. In this paper, we study the injective dimension of a complex of graded modules and derive its some properties. In particular, we define the $^*$dualizing complex for a graded ring and investigate its consequences.

We classify complactly generated t-structures on the derived category of modules over a commutative Noetherian ring R in terms of decreasing filtrations by supports on Spec(R). A decreasing filtration by supports φ : Z → Spec(R) satisfies the weak Cousin condition if for any integer i the set φ(i) contains all the inmediate generalizations of each point in φ(i+ 1). Every t-structure on Dbfg(R) ...