Joyal's CatLab Homotopical algebra

Categorical mathematics

• Set theory?

• Category theory

• Homotopical algebra

• Higher category theory

  • Theory of quasi-categories

  • Higher quasi-categories?

• Geometry?

  • Elementary geometry?

  • Differential geometry?

  • Lie theory?

  • Algebraic geometry?

  • Homotopical algebraic geometry?

• Number theory?

  • Elementary number theory?

  • Algebraic number theory?

• Algebra

  • Universal algebra?

  • Group theory?

  • Rings and modules?

  • Commutative algebras?

  • Lie algebras?

  • Representation theory?

  • Operads?

  • Homological algebra

• Logic?

  • Boolean algebra?

  • First order theory?

  • Model theory?

  • Categorical logic?

• Topology?

  • General topology

  • Algebraic topology?

  • Homotopy theory?

  • Theory of locales?

  • Topos theory?

  • Higher topos theory?

• Combinatorics?

  • Combinatorial geometry?

  • Enumerative combinatorics?

  • Algebraic combinatorics?