nLab mathematicscontents

• mathematics

  • math resources

  • history of mathematics

• Structural Foundations

  • logic

    • internal language
    • classical mathematics
    • constructive mathematics
    • predicative mathematics
    • category:foundational axiom

  • set theory

    • structural set theory

  • category theory

    • Categories and Sheaves

    • topos theory

      • Sheaves in Geometry and Logic

  • higher category theory

    • higher topos theory

      • (∞,1)-topos theory
        • models for ∞-stack (∞,1)-toposes
        • cohomology

    • homotopy theory

      • stable homotopy theory
      • rational homotopy theory

• Topology and Geometry

  • geometry (general list), topology (general list)
  • general topology
  • differential topology
  • differential geometry
    • synthetic differential geometry
    • symplectic geometry
  • algebraic geometry
  • noncommutative algebraic geometry
  • noncommutative geometry (general flavour)
  • higher geometry

• Algebra

  • universal algebra

  • higher algebra

  • homological algebra

  • group theory, ring theory

    • representation theory

  • algebraic approaches to differential calculus

  • counterexamples in algebra

• analysis

  • nonstandard analysis

  • functional analysis

    • operator algebras

  • Fourier transform

• Lie theory

  • higher Lie theory

• probability theory

• discrete mathematics