An IsProduct whose projections are genuine MORPHISMS (arrows), not merely the structural callables IsProduct checks. More...

Concept definition

template<typename P, typename A, typename B, typename Op AnyOperation>
concept dedekind::category::IsArrowProduct = 
    IsProduct<P, A, B, Op> && IsArrow<Π<1, P>> && IsArrow<Π<2, P>> &&
    std::same_as<typename Π<1, P>::Codomain, A> &&
    std::same_as<typename Π<2, P>::Codomain, B>

Detailed Description

An IsProduct whose projections are genuine MORPHISMS (arrows), not merely the structural callables IsProduct checks.

Extends IsProduct with IsArrow on the reified projections Π<1, P> / Π<2, P> (Domain = P, Codomain the corresponding part). The shared IsProduct is deliberately left structural, requiring arrow projections across all ~40 product witnesses (std::pair, Complex, Dual, ...) would be a separate 6-module refactor. The reducer nodes :lattice::Meet / Join (and their downstream sets lifts Meet / Join) target this stronger concept, so their projection type signatures are pinned to arrows with no churn to the wider ecosystem.

See also: IsProduct, Π