In this article the map given by the anticanonical bundle of a Fano manifold is investigated with respect to a number of natural notions of higher order embeddings of projective manifolds. This is of importance in the understanding of higher order embeddings of the special varieties of adjunction theory, which are usually bered by special Fano manifolds. An analysis is carried out of the higher...

Mathematical Morphology arose in 1964 by the work of George Matheron and Jean Serra, who developed its main concepts and tools. It uses concepts from algebra and geometry. (Set theory, complete lattice theory, convexity etc,). The notion of adjunction is very fundamental in Mathematical Morphology. Morphological systems is a broad class of nonlinear signal operators that have found many applica...

Any adjunction produces an epireflection in a canonical way, provided there exists a prefactorization system which factorizes all of its unit morphisms through epimorphisms. The stable units property, for the so obtained epireflections, is thereafter equivalently restated in such a manner it is easily recognizable in the examples. Furthermore, having stable units, there is a strong but quite si...

Minimalist grammars (MGs), as introduced in Stabler (1997), have proven a useful instrument in the formal analysis of syntactic theories developed within the minimalist branch of the principles–and–parameters framework (cf. Chomsky 1995, 2000). In fact, as shown in Michaelis (2001), MGs belong to the class of mildly context–sensitive grammars. Interestingly, without there being a rise in (at le...

Abstract It is well established that equational algebraic theories and the monads they generate can be used to encode computational effects. An important insight of Power Shkaravska comodels an theory $\mathbb{T}$ – i.e., models in opposite category $\mathcal{S}\mathrm{et}^{\mathrm{op}}$ provide a suitable environment for evaluating effects encoded by . As already noted Shkaravska, taking yield...

In this paper we examine a phenomenon which has proved difficult to account for using standard assumptions of current syntactic theory, namely extraposition. Starting with Rosenbaum (1967), all analyses we are aware of (with the exception of Emonds (1976)) treat extraposition as adjunction of a phrase to some right peripheral projection of a matrix sentence. This adjunction may either be analyz...

This paper describes how the structure of the state space of the quantum harmonic oscillator can be described by an adjunction of categories, that encodes the raising and lowering operators into a commutative comonoid. The formulation is an entirely general one in which Hilbert spaces play no special role. Generalised coherent states arise through the hom-set isomorphisms defining the adjunctio...

We prove a new adjunction theorem for n-equivalences. This theorem enables us to produce a simple geometric version of proof of the triad connectivity theorem of Blakers and Massey. An important intermediate step is a study of the collapsing map S∨X → S,