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LAWVERETIERNEY SHEAVES IN ALGEBRAIC SET THEORY
"... 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 LawvereTierney coverages, rather than by Grothendieck coverages, and assume ..."
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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 LawvereTierney 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 topostheoretic results.
A general construction of internal sheaves in algebraic set theory. Preliminary version available at [3
"... 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 LawvereTierney coverages, rather than by Grothendieck coverages, and assume ..."
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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 LawvereTierney 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 topostheoretic results.