dedekind::category::IsBijectiveArrow Concept Reference

An arrow declared to be both a monomorphism (ι: A ↣ B) and an epimorphism (π: A ↠ B), i.e. an isomorphism of sets (A ≅ B). More...

Concept definition

template<typename E>
concept dedekind::category::IsBijectiveArrow =  IsMonicArrow<E> && IsEpicArrow<E>

Detailed Description

An arrow declared to be both a monomorphism (ι: A ↣ B) and an epimorphism (π: A ↠ B), i.e. an isomorphism of sets (A ≅ B).

A bijective arrow is both injective and surjective. The user declares this by specialising both is_monic_arrow_v<E> = true and is_epic_arrow_v<E> = true. Identity arrows are always bijective.