The Morita equivalence for field theories on noncommutative two-tori is analysed in detail for rational values of the noncommutativity parameter θ (in appropriate units): an isomorphism is established between an abelian noncommutative field theory (NCFT) and a nonabelian theory of twisted fields on ordinary space. We focus on a particular conformal field theory (CFT), the one obtained by means ...

Let b be a block with normal abelian defect group and inertial quotient. We prove that every Morita auto-equivalence of has linear source. note this improves upon results Zhou also Boltje, Kessar Linckelmann.

We extend categorical Morita equivalence to finite tensor categories gra\-ded by a group $G$. show that two such are graded equivalent if and only their equivariant Drinfeld centers as braided $G$-crossed categories.

We show that in the generic case the smooth noncommutative tori associated to two n×n real skew-symmetric matrices are Morita equivalent if and only if the matrices are in the same orbit of the natural SO(n, n|Z) action.

Algebraic theories are called Morita equivalent provided that the corresponding varieties of algebras are equivalent. Generalizing Dukarm’s result from one-sorted theories to many-sorted ones, we prove that all theories Morita equivalent to an S-sorted theory T are obtained as idempotent modifications of T . This is analogous to the classical result of Morita that all rings Morita equivalent to...

Symplectic reduction is reinterpreted as the composition of arrows in the category of integrable Poisson manifolds, whose arrows are isomorphism classes of dual pairs, with symplectic groupoids as units. Morita equivalence of Poisson manifolds amounts to isomorphism of objects in this category. This description paves the way for the quantization of the classical reduction procedure, which is ba...

We show that the theory of MV-algebras is Morita-equivalent to that of abelian `-groups with strong unit. This generalizes the well-known equivalence between the categories of set-based models of the two theories established by D. Mundici in 1986, and allows to transfer properties and results across them by using the methods of topos theory. We discuss several applications, including a sheaf-th...

An arbitrary Lie groupoid gives rise to a groupoid of germs of local diffeomorphisms over its base manifold, known as its e ect. The e ect of any bundle of Lie groups is trivial. All quotients of a given Lie groupoid determine the same e ect. It is natural to regard the e ects of any two Morita equivalent Lie groupoids as being equivalent . In this paper we shall describe a systematic way of co...