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Title: Weak distributive laws
Related: Theory and applications of categories, Vol. 22, No. 12, (2009), p.313-320
Related: http://www.tac.mta.ca/tac/volumes/22/12/22-12abs.html
Publisher: Mount Allison University, Department of Mathematics and Science
Date: 2009
FoR/RFCD Code(s): 010100 Pure Mathematics
Author/Creator: Street, Ross
Description: 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.
Description: 8 page(s)
Subject Keyword: 010100 Pure Mathematics
Subject Keyword: monad
Subject Keyword: triple
Subject Keyword: distributive law
Subject Keyword: weak bialgebra
Resource Type: journal article
Organisation: Macquarie University. Dept. of Mathematics

Identifier: http://hdl.handle.net/1959.14/189996
Identifier: ISSN:1201-561X
Identifier: mq-rm-2009004808
Language: eng
Rights: Copyright the Author(s) [2009]. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.
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