dedekind::algebra::IsMagma Concept Reference

Proposition: a set object X whose carrier X::Domain forms a magma — the set-indexed lift of category::IsMagma. More...

Concept definition

template<typename X, typename Op std::plus<typename X::Domain>>
concept dedekind::algebra::IsMagma =  IsAlgebraOnSet<X, Op> &&
                  dedekind::category::IsMagma<typename X::Domain, Op>

Detailed Description

Proposition: a set object X whose carrier X::Domain forms a magma — the set-indexed lift of category::IsMagma.

The base rung of the algebra tower, as the set monad's image of the type-indexed category::IsMagma: X is an ETCS set (category::IsSet), its carrier X::Domain satisfies the axiomatic category::IsMagma<X::Domain, Op>, and IsAlgebraOnSet supplies the carrier discipline: IsLSet roots std::semiregular on X::Domain and IsClosedAlgebra pins strict closure under Op.

Template Parameters

X	The set object (category::IsSet).
Op	The binary operation on X::Domain (defaults to std::plus).