Closed Categories and Categorial Grammar

Inspired by Lambek's work on categorial grammar, we examine the proposal that the theory of biclosed monoidal categories can serve as a foundation for a formal theory of natural language. The emphasis throughout is on the derivation of the axioms for these categories from linguistic intuitions. When Montague's principle that there is a homomorphism between syntax and semantics is reened to the principle that meaning is a functor between a syntax-category and a semantics-category, the fundamental properties of biclosed categories induce a rudimentary computationally oriented theory of language.