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

Título:

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

Autor:

Fiore, Marcelo

Colaboradores:

; Menni, Matías

Temas:

TEORÍA DE CATEGORÍASMATEMÁTICA DE LA COMPUTACIÓN

En:

(2005) Theory and Applications of Categories, 15 (2), pp 40-65.

Resumen:

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.

URL/DOI:

Medio:

Soporte electrónico

Tipo de documento:

Artículo

Idioma:

Inglés

Publicación:

, 2005

Puede solicitar más fácilmente el ejemplar con: A0073

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