Lawvere-Tierney sheaves in algebraic set theory

Details Lawvere-Tierney sheaves in algebraic set theory Lawvere-Tierney sheaves in algebraic set theory

2007-11-09

arxiv.org/abs/0711.1529v3

Mathematics

Logic

33 pages; a revised version of the earlier paper "A general construction of internal sheaves in algebraic set theory"; accepte

Scientific paper

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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