Pseudo Functorial Semantics
نویسنده
چکیده
Categories with algebraic structure—the most prominent example being monoidal categories—satisfy equational axioms only up-to coherent isomorphisms. Therefore they are pseudo algebras. We extend Lawvere’s functorial semantics to such pseudo structure: in contrast to standard strict algebras which are identified with productpreserving functors, pseudo algebras are product-preserving pseudo functors. This identification paves a way to a uniform theory of pseudo algebras. To demonstrate its use we prove a lifting result of pseudo algebraic structure to a category of coalgebras, a result that is crucial in our coalgebraic study of software components with the microcosm principle.
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