Indeed, Lambek was one of the founders of categorical grammer, and from the article:
""" Around 2004 I was giving a talk at the McGill category Theory seminar about our then new diagrammatic description of quantum teleportation. Lambek immediately pointed out: “Those are pre-groups!” The compact closed category-theory underpinning of quantum theory, have indeed pregroups as the posetal instance. It was this connection, between grammar and teleportation diagrams, that inspired the DisCoCat model, making it look as if word-meaning being teleported around in sentences by means of the channels provided by the pregroup grammar """