A PROP is a way of encoding structure borne by an object of a symmetric monoidal category. We describe a notion of distributive law for PROPs, based on Beck's distributive laws for monads. A distributive law between PROPs allows them to be composed, and an algebra for the composite PROP consists of a single object with an algebra structure for each of the original PROPs, subject to compatibility conditions encoded by the distributive law. An example is the PROP for bialgebras, which is a composite of the PROP for coalgebras and that for algebras.
|Number of pages||17|
|Journal||Theory and Applications of Categories|
|Publication status||Published - 2004|
- Distributive law
- Symmetric monoidal category