: the FOLD notion Δ†:A×A→A --- an arrow whose Domain is the square of its Codomain (the comonoid dagger / binary combiner). Merge<A,Meet> is the canonical MODEL; this concept is the matchable handle. Purely structural: it names the A×A→A signature, so a PROJECTION π:A×A→A also satisfies it (the shape cannot tell a fold from a projection, the same honesty gap as glb-vs-lub). Same seams as IsCopy: carrier past std::pair (#951); the multi-reading dom/cod contract (#952). More...

Concept definition

template<typename F>

concept dedekind::category::IsMerge = IsArrow<F> && std::same_as<Dom<F>, std::pair<Cod<F>, Cod<F>>>

dedekind::category::IsArrow

A type that knows its own Domain (A) and Codomain (B), objects it maps between: called at the domain'...

Definition morphism.cppm:168

dedekind::category::IsMerge

: the FOLD notion Δ†:A×A→A --- an arrow whose Domain is the square of its Codomain (the comonoid dagg...

Definition cartesian_bicategory.cppm:197

dedekind::category::Cod

typename std::remove_cvref_t< F >::Codomain Cod

Shorthand to look up the Codomain of an Arrow type F.

Definition morphism.cppm:239

Detailed Description

: the FOLD notion Δ†:A×A→A --- an arrow whose Domain is the square of its Codomain (the comonoid dagger / binary combiner). Merge<A,Meet> is the canonical MODEL; this concept is the matchable handle. Purely structural: it names the A×A→A signature, so a PROJECTION π:A×A→A also satisfies it (the shape cannot tell a fold from a projection, the same honesty gap as glb-vs-lub). Same seams as IsCopy: carrier past std::pair (#951); the multi-reading dom/cod contract (#952).