A Morphism whose Codomain is the Terminal Object (One). More...

Concept definition

template<typename F>
concept dedekind::category::IsMorphicTotal =  requires {
  typename F::Domain;
  typename F::Codomain;
} && std::same_as<typename F::Codomain, One>

Detailed Description

A Morphism whose Codomain is the Terminal Object (One).

A morphism f: A → One is "morphically total" in the categorical sense: it maps every element of its domain to the unique element of One. This is the categorical analogue of a constant function that always returns std::monostate{}.

Note: This is distinct from IsTotalArrow (in :total), which concerns whether a morphism is defined on all inputs without undefined behaviour.