Algebra, Homological.

Categories (Mathematics)

Graph theory.

Modules (Algebra)

Operads.

Permutation groups.

Algebraic topology > Applied homological algebra and category theory > Topological categories, foundations of homotopy theory.

Category theory; homological algebra > Categories with structure > None of the above, but in this section.

Commutative algebra > Homological methods > Deformations and infinitesimal methods.

Quantum theory > Quantum field theory; related classical field theories > String and superstring theories; other extended objects (e.g., branes)