In this communication we generalize some recent results of Rump to categories enriched in a commutative quantale V. Using these results, show that every quantale-enriched multicategory admits an injective hull. Finally, expose connection between the Isbell adjunction and construction hulls for topological spaces made by Banaschewski 1973.

We consider some conditions under which a smooth projective variety X is actually the projective space. We also extend to the case of positive characteristic some results in the theory of vector bundle adjunction. We use methods and techniques of the so called Mori theory, in particular the study of rational curves on projective manifolds. Mathematics Subject Classification (1991): 14E30, 14J40...

We establish in this paper the link between the two main approaches for fuzzy mathematical morphology, based on duality with respect to complementation and on the adjunction property, respectively. We also prove that the corresponding definitions of fuzzy dilation and erosion are the most general ones if a set of classical properties is required.

We develop a category theoretical framework for the comprehension of the information structure associated with a complex system, in terms of families of partial or local information carriers. The framework is based on the existence of a categorical adjunction, that provides a theoretical platform for the descriptive analysis of the complex system as a process of functorial information communica...

In V2 languages subject-verb inversion is followed by obligatory topicalisation, in VSO languages it is not. I propose that verb movement in V2 languages is self-attachment, while in VSO languages it is adjunction to a VP-external head. This analysis makes predictions on typology, language acquisition and change. Evidence comes mainly from Welsh, Breton, and Early Swedish.

Consider categories with involutions which fix objects, functors which preserve involution, and natural transformations. In this setting certain natural adjunctions become universal and, thereby, become constructible from abstract data. Although the formal theory of monads fails to apply and the Eilenberg-Moore category fails to fit, both are successfully adapted to this setting, which is a 2-c...

The notion of sobriety is extended to the realm topological spaces valued in a commutative and unital quantale, via an adjunction between category quantale modules quantale-valued spaces. Relations such sober domains based on flat ideals are investigated. In particular, it shown that if unit element coincides with its top element, then every domain (relative ideals) Scott topology space.