The PI is continuing his work in the categorical foundations of the theory of computation. This work is based on recent technical advances involving topos-theoretical models of computation. Special emphasis is being placed on exposing the intrinsic functorial semantics of these models, the creation of new topos models, and the continued refinement of a synthetic theory of computation. Applications include classification and characterization of higher type functionals and new approaches to computable analysis and effective semantics. The problems proposed are important ones lying at the interface between category theory and computation theory. There is a renewed interest, both in the U.S. and internationally, in the use of category theory in the foundations of computation. This modest grant will indicate the appropriation of certain categorical tools for the explication of the foundations of computation.
