Reflective Kleisli subcategories of the category of Eilenberg-Moore algebras for factorization monads - Fiore, Marcelo (^p Datos electrónicos (1 archivo : 243 KB))
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: Combinatorial structures; Factorization systems; Joyal species; Kleisli categories; Monads; Power series; Schanuel topos.