A general construction of internal sheaves in algebraic set theory
We present a solution to the problem of defining a counterpart in Algebraic Set Theory of the construction of internal sheaves in Topos Theory. Our approach is general in that we consider sheaves as determined by Lawvere-Tierney coverages, rather than by Grothen-dieck coverages, and assume only a we...
| Autores: | ; ; ; |
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| Tipo de documento: | Artículo |
| Fecha de publicación: | 2007 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Lenguaje: | Inglés |
| OAI Identifier: | oai:ddd.uab.cat:44083 |
| Acceso en línea: | https://ddd.uab.cat/record/44083 |
| Nivel de acceso: | Acceso abierto |
| Palabra clave: | Conjunts, Teoria de Lògica matemàtica Categories (Matemàtica) |
| Sumario: | We present a solution to the problem of defining a counterpart in Algebraic Set Theory of the construction of internal sheaves in Topos Theory. Our approach is general in that we consider sheaves as determined by Lawvere-Tierney coverages, rather than by Grothen-dieck coverages, and assume only a weakening of the axioms for small maps originally introduced by Joyal and Moerdijk, thus subsuming the existing topos-theoretic results. |
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