Dear Pierre, I heard from Christian Houzel that he worked on this subject long ago but never published. He gave recently in ENS a talk on this subject, I copy his abstract below. best, Andrei Les productions des langues naturelles se présentent comme des concaténations d'éléments. On peut traduire mathématiquement la concaténation par la loi de composition d'un monoïde. Mais toute suite de mots ne constitue pas une phrase ; il faut une structure syntaxique. De telles structures constituent les morphismes d'une catégorie monoïdale. Les théories interprétatives, comme la phonologie ou la sémantique introduisent des filtres additionnels, qu'il paraît convenable de prendre en compte au moyen d'une topologie convenable. Une théorie interprétative est alors représentée par un faisceau sur un site convenable. Selon Pierre Cardascia <p.cardascia@yahoo.fr>:
Hello, dear categorists, My name is Pierre Cardascia, I'm student of mathematics and philosophie in Lille, France. last year, I wrote for my research director Shahid Rahman a paper about categorical logic; and for this year, he wants me to focus on linguistic (for some obscure but good reasons). So we decided to reintroduce my former work and to explore more and more the land of catégories. The main problem is that I haven't any clue of where I must begin such a work. I asked the neighour laboratory of linguistic : nothing. So I write you with the hope that somebody can give me some hints to guide my research : references, actual problems, advises ... it seemed, but I'm not sure, that the Montreal school worked on that subject in the past, but this information is unconfirmed ...
Thanks you !
Pierre CARDSCIA
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