  Categorical compositional distributional semantics (CCDS) allows one to
compute the meaning of phrases and sentences from the meaning of their
constituent words. A type-structure carried over from the traditional
categorial model of grammar a la Lambek becomes a 'wire-structure' that
mediates the interaction of word meanings. However, CCDS has a much richer
logical structure than plain categorical semantics in that certain words can
also be given an 'internal wiring' that either provides their entire meaning or
reduces the size their meaning space. Previous examples of internal wiring
include relative pronouns and intersective adjectives. Here we establish the
same for a large class of well-behaved transitive verbs to which we refer as
Cartesian verbs, and reduce the meaning space from a ternary tensor to a unary
one. Some experimental evidence is also provided.
