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dc.contributor.authorCliment Vidal, Joan B.-
dc.contributor.authorSoliveres Tur, Juan Carlos-
dc.description" In memory of our dear friend Fuensanta Andreu Vaillo (1955{2008)"es_ES
dc.description.abstractWe consider monads over varying categories, and by defining the morphisms of Kleisli and of Eilenberg-Moore from a monad to another and the appropriate transformations (2-cells) between morphisms of Kleisli and between morphisms of Eilenberg-Moore, we obtain two 2-categories Mndₖₗ and MndEM. Then we prove that MndKl and MndEM are, respectively, 2-isomorphic to the conjugate of Kl and to the transpose of EM, for two suitably defined 2-categories Kl and EM, related, respectively, to the constructions of Kleisli and of Eilenberg-Moore. Next, by considering those morphisms and transformations of monads that are simultaneously of Kleisli and of Eilenberg-Moore, we obtain a 2-category Mndalg, of monads, algebraic morphisms, and algebraic transformations, and, to con¯rm its naturalness, we, on the one hand, prove that its underlying category can be obtained by applying the Ehresmann-Grothendieck construction to a suitable contravariant functor, and, on the other, we provide an explicit 2-embedding of a certain 2-category, Sigpd, of many- sorted signatures (hence also of another 2-category Spfpd, of many-sorted specifications), arising from the field of many-sorted universal algebra, into a 2-category of the type Mndalg. Moreover, we investigate for the adjunctions between varying categories the counterparts of the concepts previously defined for the monads, obtaining several 2-categories of adjunc- tions, as well as several 2-functors from them to the corresponding 2-categories of monads, and all in such a way that the classical Kleisli and Eilenberg-Moore constructions are left and right biadjoints, respectively, for these 2-functors. Finally, we define a 2-category Adalg, of adjunctions, algebraic squares, and algebraic transformations, and prove that there exists a canonical 2-functor Mdalg from Adalg to Mndalg.es_ES
dc.format.extent61 p.es_ES
dc.publisherUniversidad de Extremadura, Servicio de Publicacioneses_ES
dc.rightsAttribution-NonCommercial-ShareAlike 4.0 International*
dc.subjectMorfismo de Kleislies_ES
dc.subjectMorfismo de Eilenberg-Moorees_ES
dc.subjectTransformación de Kleislies_ES
dc.subjectTransformación de Eilenberg-Moorees_ES
dc.subjectPlaza adjunta de Kleislies_ES
dc.subjectPlaza adjunta de Eilenberg- Moorees_ES
dc.subjectCuadrado algebraico de adjuncioneses_ES
dc.subjectTransformación de cuadrados algebraicoses_ES
dc.subjectMorfología algebraica de mónadases_ES
dc.subjectTransformación algebraicaes_ES
dc.subjectMorphism of Kleislies_ES
dc.subjectMorphism of Eilenberg-Moorees_ES
dc.subjectTransformation of Kleislies_ES
dc.subjectTransformation of Eilenberg-Moorees_ES
dc.subjectAdjoint square of Kleislies_ES
dc.subjectAdjoint square of Eilenberg- Moorees_ES
dc.subjectAlgebraic square of adjunctionses_ES
dc.subjectTransformation of algebraic squareses_ES
dc.subjectAlgebraic morphism of monadses_ES
dc.subjectAlgebraic transformation.es_ES
dc.titleKleisli and Eilenberg-Moore constructions as parts of biadjoint situationses_ES
dc.subject.unesco1201.07 Álgebra Homológicaes_ES
dc.subject.unesco1102.12 Cálculo Proposicionales_ES
dc.subject.unesco1102.06 Fundamentos de Matemáticases_ES
europeana.dataProviderUniversidad de Extremadura. Españaes_ES
dc.identifier.bibliographicCitationCLIMENT VIDAL, J.B. y SOLIVERES TUR, J.C. (2010). Kleisli and Eilenberg-Moore constructions as parts of biadjoint situations. Extracta Mathematicae, 25 (1), 1-61. E- ISSN 2605-5686es_ES
dc.contributor.affiliationUniversidad de Valenciaes_ES
dc.identifier.publicationtitleExtracta Mathematicaees_ES
Appears in Collections:Extracta Mathematicae Vol. 25, nº 1 (2010)

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