H is a right action \(M \times S \to M\) of the monoid (S, Op) that acting_monoid<H> names: M is a right S-set (Mac Lane and Moerdijk), an S-act (Kilp, Knauer and Mikhalev, Monoids, Acts and Categories). A left action is a right action of the opposite, Opposite<Op>. More...

Concept definition

template<typename H, typename M, typename S>
concept dedekind::category::IsRightAction = 
    std::invocable<const H&, M, S> &&
    requires(const H& h, M v, S s) {  
      { h(std::move(v), std::move(s)) } -> std::convertible_to<M>;
    } && requires { typename acting_monoid<std::remove_cvref_t<H>>::type; } &&
    IsMonoid<S, typename acting_monoid<std::remove_cvref_t<H>>::type>

Detailed Description

H is a right action \(M \times S \to M\) of the monoid (S, Op) that acting_monoid<H> names: M is a right S-set (Mac Lane and Moerdijk), an S-act (Kilp, Knauer and Mikhalev, Monoids, Acts and Categories). A left action is a right action of the opposite, Opposite<Op>.

Template Parameters

H	the action.
M	what it acts on.
S	the monoid.