Functorial Semantics for Relational Theories

11/23/2017

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by   Filippo Bonchi, et al.

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We introduce the concept of Frobenius theory as a generalisation of Lawvere's 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.