List of mathematical objects by branch

• Number theory
  • numbers, operations
• Combinatorics
  • permutations, derangements, combinations
• Set theory
  • sets, set partitions
  • functions, and relations
• Category theory
  • categories
  • functors
  • morphisms
  • objects
  • natural transformations
• Geometry
  • points, lines, line segments
  • polygons (triangles, squares, pentagons, hexagons, …), circles, ellipses, parabolas, hyperbolas
  • polyhedra (tetrahedrons, cubes, octahedrons, dodecahedrons, icosahedrons), spheres, ellipsoids, paraboloids, hyperboloids, cylinders, cones
• Graph theory
  • graphs, trees, nodes, edges
• Topology
  • closed sets
  • filters
  • neighbourhoods
  • nets
  • open sets
  • topological spaces
  • uniformities
  • manifolds
    • atlases
    • charts
• Linear algebra
  • scalars, vectors, matrices, tensors
• Abstract algebra
  • groups
  • rings, modules
  • fields, vector spaces
  • group-theoretic lattices, order-theoretic lattices

• Categories are simultaneously homes to mathematical objects and mathematical objects in their own right. In proof theory, proofs and theorems are also mathematical objects.