Journal of Symbolic Logic

Lawvere—Tierney sheaves in Algebraic Set Theory

S. Awodey, N. Gambino, P. L. Lumsdaine, and M. 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.

Article information

Source
J. Symbolic Logic Volume 74, Issue 3 (2009), 861-890.

Dates
First available in Project Euclid: 16 June 2009

Permanent link to this document
http://projecteuclid.org/euclid.jsl/1245158088

Digital Object Identifier
doi:10.2178/jsl/1245158088

Mathematical Reviews number (MathSciNet)
MR2548465

Zentralblatt MATH identifier
1183.03068

Citation

Awodey, S.; Gambino, N.; Lumsdaine, P. L.; Warren, M. A. Lawvere—Tierney sheaves in Algebraic Set Theory. Journal of Symbolic Logic 74 (2009), no. 3, 861--890. doi:10.2178/jsl/1245158088. http://projecteuclid.org/euclid.jsl/1245158088.


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