Geodesic
Reflective Kleisli subcategories of the category of Eilenberg-Moore algebras for factorization monads
Theory and applications of categories, CT2004, Tome 15 (2005), pp. 40-65

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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.

Classification : 18A25, 18A40, 18C20, 05A10
Keywords: factorization systems, monads, Kleisli categories, Schanuel topos, Joyal species, combinatorial structures, power series 
@article{TAC_2005_15_a1,
     author = {Marcelo Fiore and Matias Menni},
     title = {Reflective {Kleisli} subcategories of the category {of
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     journal = {Theory and applications of categories},
     pages = {40--65},
     publisher = {mathdoc},
     volume = {15},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2005_15_a1/}
}
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Marcelo Fiore; Matias Menni. Reflective Kleisli subcategories of the category of
Eilenberg-Moore algebras for factorization monads. Theory and applications of categories, CT2004, Tome 15 (2005), pp. 40-65. http://geodesic.mathdoc.fr/item/TAC_2005_15_a1/