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Lawvere–Tierney sheaves in Algebraic Set Theory

2009

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.

Algebraic setPure mathematicsLogicMathematics - Category TheoryMathematics - LogicTopos theoryPhilosophyMathematics::LogicMathematics::Algebraic GeometryMathematics::Category TheoryFOS: MathematicsCategory Theory (math.CT)Algebraic Set Theory sheavesLogic (math.LO)03C90 03G30 03F50AxiomMathematics
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