Re: quantum logic

[Michael Barr <barr@barrs.org>]

I will let others answer about the connection between closed monoidal
categories and MLL, but I just wanted to say that I am not sure what you
mean by the category of Hilbert spaces.  If you want the inner product
preserved, then only isometric injections are permitted.  If you want just
bounded linear maps then you are not making any real use of the inner
product.  And the spaces are self-dual, so it is not a good model of
*-autonomy.  Perhaps of compact categories, I would have to think about
it.  But anyway, you have to say what category is meant.  Another
possibility is partial isometries (which can be thought of as total by
being zero on the subspace orthognal to the domain).  This is a lot like
sets and partial injections.

Michael