Geodesic
Weak distributive laws
Theory and applications of categories, Tome 22 (2009), pp. 313-320

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

Distributive laws between monads (triples) were defined by Jon Beck in the 1960s. They were generalized to monads in 2-categories and noticed to be monads in a 2-category of monads. Mixed distributive laws are comonads in the 2-category of monads; if the comonad has a right adjoint monad, the mate of a mixed distributive law is an ordinary distributive law. Particular cases are the entwining operators between algebras and coalgebras. Motivated by work on weak entwining operators, we define and study a weak notion of distributive law for monads. In particular, each weak distributive law determines a wreath product monad (in the terminology of Lack and Street); this gives an advantage over the mixed case.

Classification : 18C15, 18D10, 18D05
Keywords: monad, triple, distributive law, weak bialgebra 
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     author = {Ross Street},
     title = {Weak distributive laws},
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     volume = {22},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2009_22_a11/}
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Ross Street. Weak distributive laws. Theory and applications of categories, Tome 22 (2009), pp. 313-320. http://geodesic.mathdoc.fr/item/TAC_2009_22_a11/