Search results for "Algebraic set theory"

showing 2 items of 2 documents

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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The associated sheaf functor theorem in algebraic set theory

2008

We prove a version of the associated sheaf functor theorem in Algebraic Set Theory. The proof is established working within a Heyting pretopos equipped with a system of small maps satisfying the axioms originally introduced by Joyal and Moerdijk. This result improves oil the existing developments by avoiding the assumption of additional axioms for small maps and the use of collection sites.

Sheaf cohomologyFunctorDirect image functorLogicInvertible sheafIdeal sheafAlgebraMathematics::LogicDerived algebraic geometryMathematics::Category TheorySheafAlgebraic set theory presheaves sheavesInverse image functorMathematics
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