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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Bibliographic Details
Authors: Awodey, Steve; Gambino, Nicola; Lumsdaine, P. L.; Warren, M. A.
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)
Description
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.