categories: Nonsymmetric closed categories

[Bill Rowan <rowan@transbay.net>]

I have been finding some nonsymmetric closed category structures on some
important categories.  By this, I mean a monoidal category, not necessarily
symmetric, such that each functor -\square b has a right adjoint.  For
example, I found a nice such structure on the category of locally closed
topological spaces, that is, spaces such that the filter of neighborhoods of
each point has a base of closed neighborhoods.

I'm probably going to write this and some other examples up and put it online
somewhere.  Does anyone know of previous work which would be relevant?  In
Mac Lanes CWM he talks about compactly generated spaces, which I have looked
at carefully, but this is a somewhat different approach to moving beyond the
locally compact Hausdorff spaces, which of course form a cartesian closed
category.  In my example, of course, the \square operation is not the product
of topological spaces, although it has a continuous map onto it.

Bill Rowan