I am pleased to announce the availability of the following extended abstract, which might be of interest to some readers of this list: Dagger compact closed categories and completely positive maps by Peter Selinger http://www.mathstat.dal.ca/~selinger/papers.html#dagger The abstract is below. Roughly speaking, dagger compact closed categories (due to Abramsky and Coecke) capture most of the interesting properties of the category of finite dimensional Hilbert spaces. This paper contributes a graphical language and a new construction. -- Peter * * * Abstract: Dagger compact closed categories were recently introduced by Abramsky and Coecke, under the name ``strongly compact closed categories'', as an axiomatic framework for quantum mechanics. We present a graphical language for dagger compact closed categories, and sketch proof of its completeness for equational reasoning. We give a general construction, the CPM construction, which associates to each dagger compact closed category its ``category of completely positive maps'', and we show that the resulting category is again dagger compact closed. We apply these ideas to Abramsky and Coecke's interpretation of quantum protocols, and to D'Hondt and Panangaden's predicate transformer semantics. -- Peter Selinger Associate Professor Department of Mathematics and Statistics University of Ottawa (until June 30, 2005) Dalhousie University (from July 1, 2005)