Abstract not found

Abstract A useful general concept of bialgebroid seems to be resolving itself in recent publications; we give a treatment in terms of modules and enriched categories. Generalizing this concept, we define the term "quantum category"in a braided monoidal category with equalizers distributed over by tensoring with an object. The definition of antipode for a bialgebroid is less resolved in the literature. Our suggestion is that the kind of dualization occurring in Barr's starautonomous categories is more suitable than autonomy ( = compactness = rigidity). This leads to our definition of quantum groupoid intended as a "Hopf algebra with several objects". 1.

Six equivalent definitions of Frobenius algebra in a monoidal category are provided. In a monoidal bicategory, a pseudoalgebra is Frobenius if and only i f it is star autonomous. Autonomous pseudoalgebras are also Frobenius. What i t means for a morphism of a bicategory to be a projective equivalence is defined; this concept is related to "strongly separable " Frobenius algebras and "weak monoidal Morita equivalence". Wreath products of Frobenius algebras are discussed.

Abstract. Ontology alignment foundations are hard to find in the literature. The abstract nature of the topic and the diverse means of practice make it difficult to capture it in a universal formal foundation. We argue that such a lack of formality hinders further development and convergence of practices, and in particular, prevents us from achieving greater levels of automation. In this article we present a formal foundation for ontology alignment that is based on interaction models between heterogeneous agents on the Semantic Web. We use the mathematical notion of information flow in a distributed system to ground our three hypotheses of enabling semantic interoperability and we use a motivating example throughout the article: how to progressively align two ontologies of research quality assessment through meaning coordination. We conclude the article with the presentation—in an executable specification language—of such an ontology-alignment interaction model. 1.

Information integration is not a new problem.

The cyclic Chu-construction for closed bicategories, generalizing the original Chu-construction for symmetric monoidal closed categories, turns out to have a non-cyclic counterpart. Both constructions are based on so-called Chu-cells and can be generalized to chains of composable 1-cells. This leads to two hierarchies of closed bicategories for any closed bicategory with local pullbacks. Chu-cells in rel correspond to bipartite state transition systems. Even though their vertical composition may fail here due to the lack of pullbacks, basic game-theoretic constructions can be performed on cyclic Chu-cells. These generalize to all symmetric monoidal closed categories. If finite limits exist, the cyclic Chu-cells form the objects of a *-autonomous category.