# On quantales that classify C*-algebras ∗

@article{Kruml2004OnQT, title={On quantales that classify C*-algebras ∗}, author={David Kruml and Pedro Resende}, journal={Cahiers de Topologie et G{\'e}om{\'e}trie Diff{\'e}rentielle Cat{\'e}goriques}, year={2004}, volume={45}, pages={287-296} }

The functor Max of Mulvey assigns to each unital C*-algebra A the unital involutive quantale Max A of closed linear subspaces of A, and it has been remarked that it classifies unital C*-algebras up to ∗-isomorphism. In this paper we provide a proof of this and of the stronger fact that for every isomorphism u : Max A → Max B of unital involutive quantales there is a ∗-isomorphism b : A → B such that Max b u coincides with u when restricted to the left-sided elements of Max A. But we also show…

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