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Internal and external aspects of continuous logic and categorical logic for sheaves over quantales
dc.rights.license | Reconocimiento 4.0 Internacional |
dc.contributor.advisor | Mariano, Hugo Luiz |
dc.contributor.advisor | Zambrano Ramírez, Pedro Hernán |
dc.contributor.author | Reyes Gaona, David |
dc.date.accessioned | 2023-11-30T14:23:58Z |
dc.date.available | 2023-11-30T14:23:58Z |
dc.date.issued | 2023 |
dc.identifier.uri | https://repositorio.unal.edu.co/handle/unal/85026 |
dc.description.abstract | In this text we explore and propose notions of sheaves over commutative, integral quantales, which are based on extensions of results of the theory of sheaves over locales: the interplay of sheaves as valued-sets and the analogy of sheaves as enriched categories. Over these proposals, we define logics that find semantics in these sheaf-like objects, on the one hand, a categorical logic that characterize the notion of sheaves associated to complete valued sets as a model of certain internal construction, and in contrast an externally defined logic whose nature is based on continuous logic for metric spaces which finds in the proposal of sheaves as enriched categories an structure for interpret the semantic. (Texto tomado de la fuente) |
dc.description.abstract | En este texto exploramos y proponemos nociones de haces sobre cuantales conmutativos e integrales, basadas en extensiones de resultados de la teoría de haces sobre locales: la interacción de los haces como conjuntos valuados y la analogía de los haces como categorías enriquecidas. Sobre estas propuestas, definimos lógicas que encuentran su semántica en estos objetos tipo haz; por un lado, una lógica categórica que caracteriza la noción de haces asociada a conjuntos valuados completos como un modelo de cierta construcción interna, y en contraste, una lógica definida externamente cuya naturaleza se basa en la lógica continua para espacios métricos, la cual encuentra en la propuesta de haces como categorías enriquecidas una estructura para interpretar su semántica. |
dc.format.extent | x, 112 páginas |
dc.format.mimetype | application/pdf |
dc.language.iso | eng |
dc.publisher | Universidad Nacional de Colombia |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ |
dc.subject.ddc | 510 - Matemáticas::514 - Topología |
dc.subject.ddc | 510 - Matemáticas::512 - Álgebra |
dc.subject.ddc | 510 - Matemáticas::511 - Principios generales de las matemáticas |
dc.subject.ddc | 510 - Matemáticas::515 - Análisis |
dc.subject.ddc | 510 - Matemáticas::511 - Principios generales de las matemáticas |
dc.subject.ddc | 510 - Matemáticas::514 - Topología |
dc.subject.ddc | 510 - Matemáticas::512 - Álgebra |
dc.subject.ddc | 510 - Matemáticas::511 - Principios generales de las matemáticas |
dc.subject.ddc | 510 - Matemáticas::515 - Análisis |
dc.subject.ddc | 510 - Matemáticas::511 - Principios generales de las matemáticas |
dc.title | Internal and external aspects of continuous logic and categorical logic for sheaves over quantales |
dc.type | Trabajo de grado - Maestría |
dc.type.driver | info:eu-repo/semantics/masterThesis |
dc.type.version | info:eu-repo/semantics/acceptedVersion |
dc.publisher.program | Bogotá - Ciencias - Maestría en Ciencias - Matemáticas |
dc.contributor.researchgroup | Interacciones Entre Teoría de Modelos, Teoría de Conjuntos, Categorías, Análisis y Geometría |
dc.description.degreelevel | Maestría |
dc.description.degreename | Maestría en Matemáticas |
dc.description.researcharea | Lógica matemática |
dc.identifier.instname | Universidad Nacional de Colombia |
dc.identifier.reponame | Repositorio Institucional Universidad Nacional de Colombia |
dc.identifier.repourl | https://repositorio.unal.edu.co/ |
dc.publisher.faculty | Facultad de Ciencias |
dc.publisher.place | Bogotá, Colombia |
dc.publisher.branch | Universidad Nacional de Colombia - Sede Bogotá |
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dc.rights.accessrights | info:eu-repo/semantics/openAccess |
dc.subject.lemb | Algebra-métodos gráficos |
dc.subject.lemb | Algebra - Graphic methods |
dc.subject.lemb | Lógica |
dc.subject.lemb | Logic |
dc.subject.proposal | Sheaves |
dc.subject.proposal | Quantales |
dc.subject.proposal | Enriched categories |
dc.subject.proposal | Metric spaces |
dc.subject.proposal | Quantale valued logic |
dc.subject.proposal | Haces |
dc.subject.proposal | Cuantales |
dc.subject.proposal | Categorías enriquecidas |
dc.subject.proposal | Espacios métricos |
dc.subject.proposal | Lógica cuantal valuada |
dc.title.translated | Aspectos internos y externos de lógica continua y lógica categórica para haces sobre cuantales |
dc.type.coar | http://purl.org/coar/resource_type/c_bdcc |
dc.type.coarversion | http://purl.org/coar/version/c_ab4af688f83e57aa |
dc.type.content | Text |
dc.type.redcol | http://purl.org/redcol/resource_type/TM |
oaire.accessrights | http://purl.org/coar/access_right/c_abf2 |
dcterms.audience.professionaldevelopment | Investigadores |
dc.contributor.researchgate | Reyes, David |
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