Functorial Semantics for Relational Theories.

We introduce the concept of Frobenius theory as a generalisation of Lawvereu0027s functorial semantics approach to categorical universal algebra. Whereas the universe for models of Lawvere theories is the category of sets and functions, or more generally cartesian categories, Frobenius theories take their models in the category of sets and relations, or more generally in cartesian bicategories.