Geodesic
Composing PROPs
Theory and applications of categories, The Carboni Festschrift, Tome 13 (2004), pp. 147-163

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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.

Classification : 18D10, 18C10, 18D35
Keywords: symmetric monoidal category, PROP, monad, distributive law, algebra, bialgebra 
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     author = {Stephen Lack},
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     year = {2004},
     language = {en},
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Stephen Lack. Composing PROPs. Theory and applications of categories, The Carboni Festschrift, Tome 13 (2004), pp. 147-163. http://geodesic.mathdoc.fr/item/TAC_2004_13_a8/