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

Detalles Bibliográficos
Autor Principal: Fiore, Marcelo
Otros autores o Colaboradores: Menni, Matías
Formato: Capítulo de libro
Lengua:inglés
Series:^p Datos electrónicos (1 archivo : 243 KB)
Temas:
Acceso en línea:tac.mta.ca/tac/volumes/15/2/15-02abs.html
Consultar en el Cátalogo
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.
Notas:Formato de archivo: PDF. -- Este documento es producción intelectual de la Facultad de Informática-UNLP (Colección BIPA / Biblioteca.) -- Disponible también en línea (Cons. 19/12/2008)

MARC

LEADER 00000naa a2200000 a 4500
003 AR-LpUFIB
005 20250423183000.0
008 230201s2005 xx o 000 0 eng d
024 8 |a DIF-M2560  |b 2650  |z DIF002462 
040 |a AR-LpUFIB  |b spa  |c AR-LpUFIB 
100 1 |a Fiore, Marcelo  |9 46353 
245 1 0 |a Reflective Kleisli subcategories of the category of Eilenberg-Moore algebras for factorization monads 
490 0 |a ^p Datos electrónicos (1 archivo : 243 KB) 
500 |a Formato de archivo: PDF. -- Este documento es producción intelectual de la Facultad de Informática-UNLP (Colección BIPA / Biblioteca.) -- Disponible también en línea (Cons. 19/12/2008) 
520 |a 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. 
534 |a (2005) Theory and Applications of Categories, 15 (2), pp 40-65. 
650 4 |a TEORÍA DE CATEGORÍAS  |9 46354 
650 4 |a MATEMÁTICA DE LA COMPUTACIÓN  |9 42939 
700 1 |a Menni, Matías  |9 44945 
856 4 0 |u tac.mta.ca/tac/volumes/15/2/15-02abs.html 
942 |c CP 
952 |0 0  |1 0  |4 0  |6 A0073  |7 3  |8 BD  |9 76901  |a DIF  |b DIF  |d 2025-03-11  |l 0  |o A0073  |r 2025-03-11 17:02:45  |u http://catalogo.info.unlp.edu.ar/meran/getDocument.pl?id=77  |w 2025-03-11  |y CP 
999 |c 52347  |d 52347