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
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Bill Rowan