6533b85efe1ef96bd12c09d3
RESEARCH PRODUCT
Lawvere–Tierney sheaves in Algebraic Set Theory
Steve AwodeyPeter Lefanu LumsdaineMichael A. WarrenNicola Gambinosubject
Algebraic setPure mathematicsLogicMathematics - Category TheoryMathematics - LogicTopos theoryPhilosophyMathematics::LogicMathematics::Algebraic GeometryMathematics::Category TheoryFOS: MathematicsCategory Theory (math.CT)Algebraic Set Theory sheavesLogic (math.LO)03C90 03G30 03F50AxiomMathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2009-09-01 |