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The purpose of the present paper is to develop in further detail the remarks, concerning the relationship of Kan functor extensions to closed structures on functor categories, made in "Enriched functor categories" | 1] §9. It is assumed that the reader is familiar with the basic results of closed category theory, including the representation theorem. Apart(More)
A useful general concept of bialgebroid seems to be resolving itself in recent publications; we give a treatment in terms of modules and enriched categories. Generalizing this concept, we define the term "quantum category"in a braided monoidal category with equalizers distributed over by tensoring with an object. The definition of antipode for a bialgebroid(More)
Strong promonoidal functors are defined. Left Kan extension (also called " existential quantification ") along a strong promonoidal functor is shown to be a strong monoidal functor. A construction for the free monoidal category on a promonoidal category is provided. A Fourier-like transform of presheaves is defined and shown to take convolution product to(More)
It is well known that strong monoidal functors preserve duals. In this short note we show that a weaker version of functor, which we call " Frobenius monoidal " , is sufficient. Further properties of Frobenius monoidal functors are developed. Throughout suppose that A and B are strict 1 monoidal categories. Definition 1. A Frobenius monoidal functor is a(More)
We discuss an inversion property of the fusion map associated to many semibialgebras. Please note that a characterisation of Hopf k-algebras has been added at the end of this version. be a symmetric (or just braided) monoidal category. A Von Neumann " core " in C is firstly a semibialgebra in C, that is, an object A in C with an associative multiplication:(More)