Minimal core part-whole relation yielding Omega. More...

Concept definition

template<typename Part, typename Whole, typename Ω bool>
concept dedekind::category::IsPartOfRelation =  requires(const Part& part, const Whole& whole) {
  requires(
      requires {
        { part <= whole } -> std::same_as<Ω>;
      } ||
      requires {
        { whole(part) } -> std::same_as<Ω>;
      } ||
      requires {
        { whole[part] } -> std::same_as<Ω>;
      });
}

Detailed Description

Minimal core part-whole relation yielding Omega.

Textbook term: primitive binary parthood predicate (often written part <= whole or part ⊑ whole depending on formalism).

This concept accepts three equivalent encodings used across partitions:

Order-style: part <= whole
Predicate-style: whole(part)
Indexer-style: whole[part]

The canonical default in IsPartRelation remains order-style (<=), while topoi/set layers may present parthood through characteristic predicates (operator()) or lookup/index syntax (operator[]).

Richer mereological structure (species routing, ambient checks, lattice refinements) should be layered by downstream partitions.

See also: https://en.wikipedia.org/wiki/Mereology