Nominal Lawvere theories

Abstract. Lawvere theories provide a category theoretic view of equa-tional logic, identifying equational theories with small categories equipped with finite products. This formulation allows equational theories to be investigated as first class mathematical entities. However, many formal systems, particularly in computer science, are described by equations modulated by side conditions asserting the “freshness of names”; these may be expressed as theories of Nominal Equational Logic (NEL). This paper develops a correspondence between NEL-theories and certain cat-egories that we call nominal Lawvere theories