We investigate universal algebra over the category Nom of nominal sets. Using the fact that Nom is a full re ective subcategory of a monadic category, we obtain an HSP-like theorem for algebras over nominal sets. We isolate a `uniform' fragment of our equational logic, which corresponds to the nominal logics present in the literature. We give semantically invariant translations of theories for nominal algebra and NEL into `uniform' theories and systematically prove HSP theorems for models of these theories.
A. Kurz and D. Petrişan, “On universal algebra over nominal sets,” Mathematical Structures in Computer Science, vol. 20, no. 02, p. 285, Apr. 2010. DOI: 10.1017/S0960129509990399
Cambridge University Press