dedekind::category::IsOrderJoinSemilattice Concept Reference

Order-theoretic join-semilattice as a commutative refinement. More...

Concept definition

template<typename T, typename Join Sup>
concept dedekind::category::IsOrderJoinSemilattice = 
    IsMereologicalJoinBand<T, Join> && IsCommutative<T, Join>

Detailed Description

Order-theoretic join-semilattice as a commutative refinement.

In the module hierarchy, :mereology provides the upstream associative + idempotent join band. :posetal refines that structure with commutativity, yielding the order-theoretic join-semilattice notion.

Note

Naming history: an IsOrderJoinSemilatticeSignature shape mixin was previously bundled into this concept's body; it was retired because IsMereologicalJoinBand transitively requires IsMereologicalJoinMagma, which already checks the operator surface (join(a, b) -> convertible_to<T>). Callsites that need just the operator-surface check use the magma concept directly.