Two Cotensors in One: Presentations of Algebraic Theories for Local State and Fresh Names

Various situations in computer science call for categories that support both cartesian closed and monoidal closed structure. Such situations include (i) models of local state, where the monoidal product describes disjointness of memory, and (ii) treatment of fresh names, as required in models of the π-calculus.I propose a technique to embed the two closed structures into one single structure. To demonstrate the technique, I show how previously studied theories of local state and fresh names can be understood formally as presentations of (enriched) algebraic theories.