Algebraic Structure & Set Operations

Primes about the basic algebraic and set-theoretic building blocks: operation properties that determine how terms combine (associativity, commutativity), abstract structures built from them (group, category), and ways collections relate (intersection, union).

10 primes in this family — primes that sit near one another in abstraction space (k-means over structural-signature embeddings). Each is shown with its short description.

• Addition — Combine two or more quantities, elements, contributions or increments through a typed binary operation that produces their sum.
• Associativity — Grouping does not affect result.
• Category — Describe a system by its arrows and their composition, not by what its objects are.
• Commutativity — Order of inputs does not affect output.
• Disjoint union — Combine collections while tagging every member with its source so equal values from different sources remain distinct in the result.
• Group — A set with an associative operation, identity, and inverses — reversible composable transformations.
• Intersection — The elements common to all of several collections.
• Jacobi identity — A skew bracket's three cyclic nestings cancel, making each element's adjoint action behave as a derivation and allowing local pairwise generators to compose into coherent higher-order structure.
• Permutation — Reassign every member or position of a collection exactly once, preserving membership while changing arrangement; the resulting bijective self-maps compose, invert, and decompose into cycles.
• Union — The elements belonging to at least one of several collections — everything that is in any of them.