A map on T carries the unit of Op to the unit of Op2, \(f(e) = e'\), computed at the one unit: the comparison is a template argument, so a map that is no constexpr function object is refused rather than an error. The unit half of a monoid homomorphism, and of a homomorphism of any signature whose operations have units. More...

Concept definition

template<typename F, typename T, typename Op, typename Op2 Op>
concept dedekind::category::PreservesUnit = 
    std::default_initializable<std::remove_cvref_t<F>> && requires {
      requires std::bool_constant<(
          std::remove_cvref_t<F>{}(unit<T>(std::remove_cvref_t<Op>{})) ==
          unit<detail_morphism::image_t<F, T>>(
              std::remove_cvref_t<Op2>{}))>::value;
    }

Detailed Description

A map on T carries the unit of Op to the unit of Op2, \(f(e) = e'\), computed at the one unit: the comparison is a template argument, so a map that is no constexpr function object is refused rather than an error. The unit half of a monoid homomorphism, and of a homomorphism of any signature whose operations have units.

Template Parameters

F	the map.
T	its carrier.
Op
Op2	the operations.