Date of Original Version

11-9-2007

Type

Article

Rights Management

All Rights Reserved

Abstract or Description

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.

DOI

10.2178/jsl/1245158088

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Philosophy Commons

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