Hommage à André Girard

Hommage to reactive psychosis.

When looking back in the history of psychiatry, the concept of reactivity had very variable impact on ethiological considerations. If classification of mental disorders is taken as a proxy, it seems that this impact is presently at the lowest that it has been in the last hundred years. The author gives a short historical overview of concept of reactive psychosis, followed by a description of th...

Girard Couples of Quantales

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.

The Girard-Reynolds Isomorphism

ion Theorem x1 : A1, . . . , xn : An ` t : B in F2 ⇒ (x1, x1) ∈ A ∗‡ 1 , . . . , (xn, x ′ n) ∈ A∗‡ n ` (|t|, |t|′) ∈ B∗‡ in P2

A conjecture of Yves André . ∗

The introduction to [2] (and references contained therein) contains a comprehensive exposition of terminology and notations relative to this conjecture. Since we use the same terminology and notations, we do not reproduce them here. The introduction to [2] also contains an exposition of results on this conjecture obtained before the article [3] came out. In this article we prove the following t...

François Bach and André Herbelin