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...
| Authors: | ; ; ; |
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| Format: | Article |
| Publication date: | 2007 |
| Country: | España |
| Institution: | Universitat Autònoma de Barcelona |
| Repository: | Dipòsit Digital de Documents de la UAB |
| Language: | English |
| OAI Identifier: | oai:ddd.uab.cat:44083 |
| Online Access: | https://ddd.uab.cat/record/44083 |
| Access Level: | Open access |
| Keyword: | Conjunts, Teoria de Lògica matemàtica Categories (Matemàtica) |
| Summary: | 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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