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Lawvere–Tierney sheaves in Algebraic Set Theory
Published online by Cambridge University Press: 12 March 2014
Abstract
We present a solution to the problem of denning 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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- Copyright © Association for Symbolic Logic 2009
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