New techniques for constructing a distributive law of a monad over another are studied using submonads, quotient monads, product monads, recursively-defined distributive laws, and linear equations. Sequel papers will consider distributive laws in closed categories and will construct monad approximations for compositions which fail to be a monad.
Keywords: distributive law, linear equation
2000 MSC: 18C15, 18C20
Theory and Applications of Categories,
Vol. 18, 2007,
No. 7, pp 172-208.
http://www.tac.mta.ca/tac/volumes/18/7/18-07.dvi
http://www.tac.mta.ca/tac/volumes/18/7/18-07.ps
http://www.tac.mta.ca/tac/volumes/18/7/18-07.pdf
ftp://ftp.tac.mta.ca/pub/tac/html/volumes/18/7/18-07.dvi
ftp://ftp.tac.mta.ca/pub/tac/html/volumes/18/7/18-07.ps