Abstract:
In this talk, based on joint work with Michael Barr and Bob Raphael, the category of vector spaces over a fixed field is used to illustrate (and, in effect, to define) the notion of a closed symmetric monodial category. Similarly, Mackey's approach to topological vector spaces is used to illustrate the chu construction.
We use this construction to explore the category of topological sup semilattices by examining the continuous morphisms into the two-point semilattice with the Sierpinski topology (with the bottom element open). We obtain some duality results and characterize the reflexive objects, which form a *-autonomous category