In order to give equal weight to syntactic and semantic considerations, we can set up a categorial grammar as a pair of calculi linked by a compositional interpretation: a syntactic source calculus, a semantic target calculus, and a homomorphism mapping types and derivations of the source to the corresponding types and derivations of the target. In this section, we work out this architecture for the standard Lambek calculi. In the following section, we will see how the extended categorial type logics reflect different views on the division of labour between syntax and semantics, and hence on the amount of work that has to be done to achieve a compositional mapping between the two.