Search results for " 03G30"

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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Polynomial functors and polynomial monads

2009

We study polynomial functors over locally cartesian closed categories. After setting up the basic theory, we show how polynomial functors assemble into a double category, in fact a framed bicategory. We show that the free monad on a polynomial endofunctor is polynomial. The relationship with operads and other related notions is explored.

Pure mathematicsPolynomialFunctorGeneral MathematicsMathematics - Category Theory18C15 18D05 18D50 03G30517 - AnàlisiMonad (functional programming)BicategoryMathematics::Algebraic TopologyCartesian closed categoryMathematics::K-Theory and HomologyMathematics::Category TheoryPolynomial functor polynomial monad locally cartesian closed categories W-types operadsFOS: MathematicsPolinomisCategory Theory (math.CT)Mathematics
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