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arXiv · 0711.1529

Lawvere-Tierney sheaves in algebraic set theory

Steve Awodey·Nicola Gambino·Peter L. Lumsdaine·Michael A. Warren
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Abstract

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 Grothendieck 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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Steve Awodey, Nicola Gambino, Peter L. Lumsdaine, Michael A. Warren. 2008-10-22. Lawvere-Tierney sheaves in algebraic set theory. https://doi.org/10.2178/jsl%2F1245158088

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