Let V be a vertex operator algebra and g an automorphism of order T . We construct a sequence of associative algebras Ag,n(V ) with n ∈ 1 T Z nonnegative such that Ag,n(V ) is a quotient of Ag,n+1/T (V ) and a pair of functors between the category of Ag,n(V )-modules which are not Ag,n−1/T (V )-modules and the category of admissible V -modules. These functors exhibit a bijection between the sim...

For a symmetric monoidal-closed category V and a suitable monad T on the category of sets, we introduce the notion of reflexive and transitive (T,V)-algebra and show that various old and new structures are instances of such algebras. Lawvere’s presentation of a metric space as a V-category is included in our setting, via the Betti-Carboni-Street-Walters interpretation of a V-category as a monad...

Verbal fluency tests are employed regularly during neuropsychological assessments of older adults, and deficits are a common finding in patients with Alzheimer's disease (AD). Little extant research, however, has investigated verbal fluency ability and subtypes in preclinical stages of neurodegenerative disease. We examined verbal fluency performance in 107 older adults with amnestic mild cogni...

Extending existing work on the conditional automaticity of category activation, the present research investigated the extent to which category activation is moderated by the resolution of visual attention. As visual attention gates access to material in semantic memory, so too should it regulate the activation of social categories when triggering verbal labels are encountered. Accordingly, only...

There is a universal component to the semantics of reduplication, which can be expressed as a radial category of concepts. I present this radial category, along with supporting evidence from a range of languages, and motivations for the links between the various senses. The structure of the radial graph gives rise to a number of predicted implicational universals. I also show that the radial ca...

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 C2-cofinite. We announce a proof of the Verlinde conjecture for V , that is, of the statement that the matrices formed by the fusion rules amo...

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 C2-cofinite. We announce a proof of the Verlinde conjecture for V , that is, of the statement that the matrices formed by the fusion rules amo...