Brian Day
*-Autonomous categories were initially defined by M. Barr to describe a type of duality carried by many monoidal closed categories. Later they were generalised by the current author to include *-autonomous promonoidal categories. Together,…
As a development of [2] and [3], we construct a "VN-bialgebra" in Vect_k for each k-linear split-semigroupal functor from a suitable monoidal category C to Vect_k. The main aim here is to avoid the customary compactness assumptions on…
Here we describe three straightforward examples of what was called a graphic Fourier transformation in [4]. At least two of these examples may be viewed simply as monoidal comonads on suitable monoidal closed functor categories, but the…
We note an inversion property of the fusion map associated to many semibialgebras.
We describe what might be called the "Hall-fusion" bialgebra constructed from a promonoidal double, and mention the corresponding face version for probicategories.
It is well known that strong monoidal functors preserve duals. In this short note we show that a slightly weaker version of functor, which we call "Frobenius monoidal", is sufficient.
We show that the (co)endomorphism algebra of a sufficiently separable "fibre" functor into Vect_k, for k a field of characteristic 0, has the structure of what we call a "unital" von Neumann core in Vect_k. For Vect_k, this particular…
We briefly relate the existence of a middle-four interchange map in a category with two monoidal structures, to the standard Cockett and Seely notion of a weakly distributive category.
We describe a sufficient condition for the process of left Kan extension to be a conservative functor. This is useful in the study of graphic Fourier transforms and quantum categories and groupoids.
We describe a $\C$-linear additive *-autonomous category of Banach spaces. Please note that a correction has been appended to the original version 1 which is maintained here for reference. Also, a proposed example of a *-autonomous category…
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. We define the term "quantum category". The definition of antipode for a…