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...

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Detalles Bibliográficos
Autores: Awodey, Steve, Gambino, Nicola, Lumsdaine, P. L., Warren, M. A.
Tipo de recurso: artículo
Fecha de publicación:2007
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:44083
Acceso en línea:https://ddd.uab.cat/record/44083
Access Level:acceso abierto
Palabra clave:Conjunts, Teoria de
Lògica matemàtica
Categories (Matemàtica)
Descripción
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.