Enumeration of mathematical structures

Mathematical structures include

• Unstructured collections

  • set

    • empty set

    • singleton set

    • unordered pair

  • bag, multiset

• Structured collections

  • list, sequence

  • tuple

    • n-tuple, n > 1

    • order pair, 2-tuple

    • triple, 3-tuple

  • tree

  • graph

    • directed

    • undirected

• Algebraic structures

  • group-like structures

    • magma

    • semigroup

    • monoid

    • group

    • Abelian group

    • groupoid

    • setoid

    • loop

    • quandrel

    • quasigroup

    • Lie group

    • symmetry group

    • Poincaré group

    • point group

  • ring-like structures

    • ring

    • semiring

    • rng

  • field-like structures

    • field

    • semifield

• Categorical structures

  • category

    • small category

    • nCat

• Other structures

  • measure

  • topology

  • metric structure

    • geometry

  • order

  • event

  • equivalence relation

  • differential structure