We introduce a description of the algebras for a monad in terms of extension systems, similar to the one for monads given by Manes. We rewrite distributive laws for monads and wreaths in terms of this description, avoiding the iteration of the functors involved. We give a profunctorial explanation of why Manes' description of monads in terms of extension systems works.
Keywords: extension systems, monads, distributive laws, wreaths, profunctors
2000 MSC: 18C15, 18C20, 18D05
Theory and Applications of Categories,
Vol. 24, 2010,
No. 4, pp 84-113.
http://www.tac.mta.ca/tac/volumes/24/4/24-04.dvi
http://www.tac.mta.ca/tac/volumes/24/4/24-04.ps
http://www.tac.mta.ca/tac/volumes/24/4/24-04.pdf
ftp://ftp.tac.mta.ca/pub/tac/html/volumes/24/4/24-04.dvi
ftp://ftp.tac.mta.ca/pub/tac/html/volumes/24/4/24-04.ps