#
Reflective Kleisli subcategories of the category of
Eilenberg-Moore algebras for factorization monads

##
Marcelo Fiore and Matias Menni

It is well known that for any monad, the associated Kleisli category
is embedded in the category of Eilenberg-Moore algebras as the free
ones. We discovered some interesting examples in which this embedding
is reflective; that is, it has a left adjoint. To understand this
phenomenon we introduce and study a class of monads arising from
factorization systems, and thereby termed factorization monads. For
them we show that under some simple conditions on the factorization
system the free algebras are a full reflective subcategory of the
algebras. We provide various examples of this situation of a
combinatorial nature.

Keywords:
factorization systems, monads, Kleisli categories,
Schanuel topos, Joyal species, combinatorial structures, power
series

2000 MSC:
18A25, 18A40, 18C20, 05A10

*Theory and Applications of Categories,*
Vol. 15, CT2004,
No. 2, pp 40-65.

http://www.tac.mta.ca/tac/volumes/15/2/15-02.dvi

http://www.tac.mta.ca/tac/volumes/15/2/15-02.ps

http://www.tac.mta.ca/tac/volumes/15/2/15-02.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/15/2/15-02.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/15/2/15-02.ps

TAC Home