Girard couples of quantales

Details Girard couples of quantales Girard couples of quantales

2008-03-06

arxiv.org/abs/0803.0853v1

Mathematics

Category Theory

Scientific paper

We introduce the concept of a Girard couple, which consists of two (not
necessarily unital) quantales linked by a strong form of duality. The two basic
examples of Girard couples arise in the study of endomorphism quantales and of
the spectra of operator algebras. We construct, for an arbitrary sup-lattice
$S$, a Girard quantale whose right-sided part is isomorphic to $S$.

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