It is known since 1973 that Lawvere’s notion of (Cauchy-)complete enriched category is meaningful for metric spaces: it captures exactly Cauchy-complete metric spaces. In this paper we introduce the corresponding notion of Lawvere completeness for (T,V)-categories and show that it has an interesting meaning for topological spaces and quasi-uniform spaces: for the former ones means weak sobriety...

repetition is one technique in language of poetry through which a word or phrase has various technical implications that impress the reader. the skillful poet, who can direct the word to be worthwhile and sensuous, is able to do that work.the value of this kind of repetition rises due to its implications where the poet owns verbal and emotional originality. if there is any defect in his talent,...

We define higher Frobenius-Schur indicators for objects in linear pivotal monoidal categories. We prove that they are category invariants, and take values in the cyclotomic integers. We also define a family of natural endomorphisms of the identity endofunctor on a k-linear semisimple rigid monoidal category, which we call the Frobenius-Schur endomorphisms. For a k-linear semisimple pivotal mono...

The meaning and lexical category of so-called verbal roots is one aspect of the voice systems in Tagalog and other Philippine-type languages which has received little attention in the controversy surrounding the analysis of these systems. It is common to assume that these roots cannot occur without any affixation and that, therefore, they should be considered precategorial. Here it is shown tha...

Let V be a simple vertex operator algebra satisfying the following conditions: (i) V(n)) = 0 for n < 0, V(0)=C1, and the contragredient module V' is isomorphic to V as a V-module; (ii) every N-gradable weak V-module is completely reducible; (iii) V is C(2)-cofinite. We announce a proof of the Verlinde conjecture for V, that is, of the statement that the matrices formed by the fusion rules among...

Despite a large number of studies on fluency disorders in schizophrenia, it is still not clear whether executive functioning and fluency tasks are empirically linked and how symptomatology could specifically get involved on these influences. We carried out analyses of performances in several verbal fluency tasks, a non-verbal fluency task and an executive test (FAB) in 25 schizophrenics and 25 ...

Given a sufficiently nice collection of sheaves on an algebraic variety V , Bondal explained how to build a quiver Q along with an ideal of relations in the path algebra of Q such that the derived category of representations of Q subject to these relations is equivalent to the derived category of coherent sheaves on V . We consider the case in which these sheaves are all locally free and study ...

The features of a usual conformal field theory were captured by the formalism of a tensor or fusion category. The notion of a Verlinde algebra which arises from a fusion category, the action of a modular group on the algebra, and the Verlinde formula gave us beautiful means to study these theories. Such they were that in [Ki] Kirillov put forth the notion of a G-equivariant fusion category so t...