Equivalence classes of exact module categories over graded tensor categories

Fuzzy projective modules and tensor products in fuzzy module categories

Let $R$ be a commutative ring. We write $mbox{Hom}(mu_A, nu_B)$ for the set of all fuzzy $R$-morphisms from $mu_A$ to $nu_B$, where $mu_A$ and $nu_B$ are two fuzzy $R$-modules. We make$mbox{Hom}(mu_A, nu_B)$ into fuzzy $R$-module by redefining a function $alpha:mbox{Hom}(mu_A, nu_B)longrightarrow [0,1]$. We study the properties of the functor $mbox{Hom}(mu_A,-):FRmbox{-Mod}rightarrow FRmbox{-Mo...

fuzzy projective modules and tensor products in fuzzy module categories

let $r$ be a commutative ring. we write $mbox{hom}(mu_a, nu_b)$ for the set of all fuzzy $r$-morphisms from $mu_a$ to $nu_b$, where $mu_a$ and $nu_b$ are two fuzzy $r$-modules. we make$mbox{hom}(mu_a, nu_b)$ into fuzzy $r$-module by redefining a function $alpha:mbox{hom}(mu_a, nu_b)longrightarrow [0,1]$. we study the properties of the functor $mbox{hom}(mu_a,-):frmbox{-mod}rightarrow frmbox{-mo...

Module Categories over Pointed Hopf Algebras

We develop some techniques for studying exact module categories over some families of pointed finite-dimensional Hopf algebras. As an application we classify exact module categories over the tensor category of representations of the small quantum groups uq(sl2).

Communications in Algebra, 9(15), 1455-1477 (1981) Morita Equivalence of Module Categories with Tensor Products

Duality and Equivalence of Module Categories in Noncommutative Geometry

We develop a general framework to describe dualities from algebraic, differential, and noncommutative geometry, as well as physics. We pursue a relationship between the Baum-Connes conjecture in operator K-theory and derived equivalence statements in algebraic geometry and physics. We associate to certain data, reminiscent of spectral triple data, a differential graded category in such a way th...