A SYNTACTIC CHARACTERIZATION OF MORITA EQUIVALENCE

A Syntactic characterization of Morita Equivalence

ul 2 01 5 A SYNTACTIC CHARACTERIZATION OF MORITA EQUIVALENCE

We characterize Morita equivalence of theories in the sense of Johnstone in [24] in terms of a new syntactic notion of a common definitional extension developed by Barrett and Halvorson in [25] for cartesian, regular, coherent, geometric and first-order theories. This provides a purely syntactic characterization of the relation between two theories that have equivalent categories of models natu...

A characterization of Morita equivalence pairs

We characterize the pairs of operator spaces which occur as pairs of Morita equivalence bimodules between non-selfadjoint operator algebras in terms of the mutual relation between the spaces. We obtain a characterization of the operator spaces which are completely isometrically isomorphic to imprimitivity bimodules between some strongly Morita equivalent (in the sense of Rieffel) C*-algebras. A...

A characterization of Morita equivalence pairs of quantales

We characterize the pairs of sup-lattices which occur as pairs of Morita equivalence bimodules between quantales in terms of the mutual relation between the sup-lattices.

Noncommutative fermions and Morita equivalence

We study the Morita equivalence for fermion theories on noncommutative two-tori. For rational values of the θ parameter (in appropriate units) we show the equivalence between an abelian noncommutative fermion theory and a nonabelian theory of twisted fermions on ordinary space. We study the chiral anomaly and compute the determinant of the Dirac operator in the dual theories showing that the Mo...