Geodesic
Weak distributive laws
Theory and applications of categories, Tome 22 (2009), pp. 313-320 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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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},
     journal = {Theory and applications of categories},
     pages = {313--320},
     year = {2009},
     volume = {22},
     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/