September 2009 Lawvere—Tierney sheaves in Algebraic Set Theory
S. Awodey, N. Gambino, P. L. Lumsdaine, M. A. Warren
J. Symbolic Logic 74(3): 861-890 (September 2009). DOI: 10.2178/jsl/1245158088

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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S. Awodey. N. Gambino. P. L. Lumsdaine. M. A. Warren. "Lawvere—Tierney sheaves in Algebraic Set Theory." J. Symbolic Logic 74 (3) 861 - 890, September 2009. https://doi.org/10.2178/jsl/1245158088

Information

Published: September 2009
First available in Project Euclid: 16 June 2009

zbMATH: 1183.03068
MathSciNet: MR2548465
Digital Object Identifier: 10.2178/jsl/1245158088

Rights: Copyright © 2009 Association for Symbolic Logic

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Vol.74 • No. 3 • September 2009
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