dedekind::category::IsLeftAction Concept Reference

The shape of a left action (S ⟳ M), \(S \times M \to M\), scalar first, as a module's: its laws are the certificate a concept above it reads (is_linear_action for a semimodule). A left action of a monoid \(M\) is a right action (IsRightAction) of its opposite, Opposite<Op> (:involution), and over a commutative monoid the two coincide. More...

Concept definition

template<typename S, typename M, typename Act std::multiplies<>>
concept dedekind::category::IsLeftAction =  requires(S s, M m) {
  requires(
      requires {
        
        { s(m) } -> std::same_as<M>;
      } ||
      requires {
        
        { Act{}(s, m) } -> std::same_as<M>;
      });
}

Detailed Description

The shape of a left action (S ⟳ M), \(S \times M \to M\), scalar first, as a module's: its laws are the certificate a concept above it reads (is_linear_action for a semimodule). A left action of a monoid \(M\) is a right action (IsRightAction) of its opposite, Opposite<Op> (:involution), and over a commutative monoid the two coincide.

Template Parameters

S	The scalar/influencer species.
M	The acted-on species.
Act	External action witness (defaults to std::multiplies<>).

Supports both textbook forms:

1. callable action object s(m)
2. binary action witness Act{}(s, m)