mathematics

Structural Foundations

• logic

  • internal language
  • classical mathematics
  • evil
  • 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