The present paper introduces aggregative spaces and their category AGS, and then establishes a dual adjunction between AGS and the category Agop of aggregation operators on bounded partially ordered sets. Spatial aggregation operators and sober aggregative spaces, enabling us to restrict the dual adjunction between AGS and Agop to a dual equivalence between the full subcategory of Agop consisti...

We report on some recent progress in the classification of smooth projective varieties with small invariants. This progress is mainly due to the finer study of the adjunction mapping by Reider, Sommese and Van de Ven [So1], [VdV], [Rei], [SV]. Adjunction theory is a powerful tool for determining the type of a given variety. Classically, the adjunction process was introduced by Castelnuovo and E...

This paper gives a systematic account of various metrics on probability distributions (states) and on predicates. These metrics are described in a uniform manner using the validity relation between states and predicates. The standard adjunction between convex sets (of states) and effect modules (of predicates) is restricted to convex complete metric spaces and directed complete effect modules. ...

There are two salient linguistic uses of adjunction: for analyzing long-distance wh-movement (and related movement types) in many languages and for analyzing cross-serial dependencies (CSD) in Dutch and Swiss German. While the need for and the adequacy of adjunction to model wh-type movement have been questioned (Rambow and Vijay-Sbanker, 1998; Rambow et al., 2001), CSD seems ideally suited for...

In this paper we will introduce and develop a theory of adjunction spaces which allows the construction non-Hausdorff topological manifolds from standard Hausdorff ones. This is done by gluing along homeomorphic open submanifolds whilst leaving boundaries these regions unidentified. case that have boundaries, it shown violation occurs precisely at boundaries. We then use formalism to provide pa...

The Eilenberg-Moore constructions and a Beck-type theorem for pairs of monads are described. More specifically, a notion of a Morita context comprising of two monads, two bialgebra functors and two connecting maps is introduced. It is shown that in many cases equivalences between categories of algebras are induced by such Morita contexts. The Eilenberg-Moore category of representations of a Mor...

We report on some recent progress in the classification of smooth projective varieties with small invariants. This progress is mainly due to the finer study of the adjunction mapping by Reider, Sommese and Van de Ven [So1], [VdV], [Rei], [SV]. Adjunction theory is a powerful tool for determining the type of a given variety. Classically, the adjunction process was introduced by Castelnuovo and E...