Related papers: Morita bundle gerbes
This thesis reviews the theory of bundle gerbes and then examines the higher dimensional notion of a bundle 2-gerbe. The notion of a bundle 2-gerbe connection and 2-curving are introduced and it is shown that there is a class in…
We present the rudiments of the Morita theory of module systems (over semirings), paralleling the classical Morita theory over associative rings.
This thesis develops the theory of bundle gerbes and examines a number of useful constructions in this theory. These allow us to gain a greater insight into the structure of bundle gerbes and related objects. Furthermore they naturally lead…
We study Morita theory of twisted sheaves on $\mu_{n}$-gerbes of line bundles $\mathscr{X}$. In this context, we find explicit equivalent conditions for when two Azumaya algebras on $\mathscr{X}$ are Morita equivalent. Additionally, we…
This is a mostly self-contained survey article about bundle gerbes and some of their recent applications in geometry, field theory, and quantisation. We cover the definition of bundle gerbes with connection and their morphisms, and explain…
We consider how Morita equivalences are compatible with the notion of a corner subring. Namely, we outline a canonical way to replace a corner subring of a given ring with one which is Morita equivalent, and look at how such an equivalence…
We prove a group graded Morita equivalences version of the "butterfly theorem" on character triples. This gives a method to construct an equivalence between block extensions from another related equivalence.
We develop the basics of Morita theory for super rings. As an application, we produce a more explicit super Morita equivalence in the case of super Azumaya algebras.
In this article we review recent developments on Morita equivalence of star products and their Picard groups. We point out the relations between noncommutative field theories and deformed vector bundles which give the Morita equivalence…
We consider a variant of the notion of Morita equivalence appropriate to weak* closed algebras of Hilbert space operators, which we call {\em weak Morita equivalence}. We obtain new variants, appropriate to the dual algebra setting, of the…
We characterize the inverse semigroups that are Morita equivalent to graph inverse semigroups. We also consider a generalization to inverse semigroups associated with left cancellative categories.
Taking advantage of the quantale-theoretic description of \'etale groupoids we study principal bundles, Hilsum-Skandalis maps, and Morita equivalence in terms of modules on inverse quantal frames. The Hilbert module description of quantale…
Logicians and philosophers of science have proposed various formal criteria for theoretical equivalence. In this paper, we examine two such proposals: definitional equivalence and categorical equivalence. In order to show precisely how…
We develop Morita theory of monoids in a closed symmetric monoidal category, in the context of enriched category theory.
The notion of a higher bundle gerbe is introduced to give a geometric realization of the higher degree integral cohomology of certain manifolds. We consider examples using the infinite dimensional spaces arising in gauge theories.
Bundle gerbes are a higher version of line bundles, we present nonabelian bundle gerbes as a higher version of principal bundles. Connection, curving, curvature and gauge transformations are studied both in a global coordinate independent…
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.
In this paper we present some key moments in the history of Morita equivalence for operator algebras.
We develop the Morita theory of fusion 2-categories. In order to do so, we begin by proving that the relative tensor product of modules over a separable algebra in a fusion 2-category exists. We use this result to construct the Morita…
Morita theory for quantales is developed. The main result of the paper is a characterization of those quantaloids (categories enriched in the symmetric monoidal closed category of sup-lattices) that are equivalent to modular categories over…