A Categorical Setting for Lower Complexity

A polarized strong category consists of a cartesian category, X, and a category Y, together with a module M:X×Y→Y equipped with a strong composition and identities. These categories can be used to provide an abstract setting for investigating computational setting with complexity below primitive recursive. This paper develops the theory of polarized strong categories, explains how they relate to the theory of fibrations, and provides a concrete example which illustrates their applicability to these lower complexity systems of computation.