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35 p, 322.4 KB A general construction of internal sheaves in algebraic set theory / Awodey, Steve ; Gambino, Nicola ; Lumsdaine, P. L. ; Warren, M. A. ; Centre de Recerca Matemàtica
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 Grothen-dieck 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.
Centre de Recerca Matemàtica 2007 (Prepublicacions del Centre de Recerca Matemàtica ; 775)  

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1 Lumsdaine, P. L.
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