We introduce a new deenition of the (Lusternik-Schnirelmann) co-category of a CW complex X. This is accomplished by producing a dual of the fat wedge called the thin product. One then looks at fac-torizations of the fold map through the thin product analogously to the Whitehead deenition of category. We investigate the relationship between this deenition and the rational cocategory introduced b...

A special case of a theorem due to Orlov states that for a hypersurface X ⊂ Pn−1 of degree n given by the equation W = 0, there exists an equivalence between the bounded derived category D(cohX) of coherent sheaves on X and the homotopy category HMF(W ) of graded matrix factorizations. We first give a description of this result, and present some methods for doing calculations with it. In the la...

In [9] a new class of MV -algebras with product, called LΠqalgebras, has been introduced. In these algebras, the discontinuous product residuation →π defined in [4] is replaced by a continuous approximation of it. These algebras seem to be a good compromise between the need of expressiveness and the need of continuity of connectives. Following a good tradition in many-valued logic (see e.g. [10...

Consumers often anthropomorphize brands by endowing them with personality traits, and marketers often create or reinforce these perceptions by their brand positioning. Brand personality traits provide symbolic meaning or emotional value that can contribute to consumers’ brand preferences and can be more enduring than functional attributes. Successfully positioning a brand’s personality within a...

Abstract. We present a categorical model for intuitionistic linear logic where objects are polynomial diagrams and morphisms are simulation diagrams. The multiplicative structure (tensor product and its adjoint) can be defined in any locally cartesian closed category, whereas the additive (product and coproduct) and exponential (⊗-comonoid comonad) structures require additional properties and a...

We analyze the algebraic structure of the Connes fusion tensor product (CFTP) in the case of bi-finite Hilbert modules over a von Neumann algebra M . It turns out that all complications in its definition disappear if one uses the closely related bi-modules of bounded vectors. We construct an equivalence of monoidal categories with duality between a category of Hilbert bi-modules over M with CFT...