Internal and external aspects of continuous logic and categorical logic for sheaves over quantales
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 logi...
- Autores:
-
Reyes Gaona, David
- Tipo de recurso:
- Fecha de publicación:
- 2023
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/85026
- Palabra clave:
- 510 - Matemáticas::514 - Topología
510 - Matemáticas::512 - Álgebra
510 - Matemáticas::511 - Principios generales de las matemáticas
510 - Matemáticas::515 - Análisis
510 - Matemáticas::511 - Principios generales de las matemáticas
510 - Matemáticas::514 - Topología
510 - Matemáticas::512 - Álgebra
510 - Matemáticas::511 - Principios generales de las matemáticas
510 - Matemáticas::515 - Análisis
510 - Matemáticas::511 - Principios generales de las matemáticas
Algebra-métodos gráficos
Lógica
Algebra - Graphic methods
Logic
Sheaves
Quantales
Enriched categories
Metric spaces
Quantale valued logic
Haces
Cuantales
Categorías enriquecidas
Espacios métricos
Lógica cuantal valuada
- Rights
- openAccess
- License
- Reconocimiento 4.0 Internacional
| Summary: | 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) |
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