An arrow declared to be an epimorphism (π: A ↠ B). More...

Concept definition

template<typename E>

concept dedekind::category::IsEpicArrow = IsArrow<E> && (is_epic_arrow_v<E> || IsIsomorphism<E>)

dedekind::category::IsArrow

A type that knows its own Domain (A) and Codomain (B), objects it maps between: called at the domain'...

Definition morphism.cppm:168

dedekind::category::IsEpicArrow

An arrow declared to be an epimorphism (π: A ↠ B).

Definition morphism.cppm:1183

dedekind::category::IsIsomorphism

An Arrow f: A -> B with a guaranteed Inverse g: B -> A.

Definition morphism.cppm:1010

dedekind::category::is_epic_arrow_v

constexpr bool is_epic_arrow_v

User-declared epicity witness for an arrow type.

Definition morphism.cppm:1166

Detailed Description

An arrow declared to be an epimorphism (π: A ↠ B).

An epic arrow is surjective: for every b in B there exists a in A with e(a) == b. The user declares epicity via is_epic_arrow_v<E> = true.

An IsIsomorphism is epic for free, symmetrically to IsMonicArrow: a two-sided inverse makes it surjective. So an iso is both monic and epic without a separate opt-in, and IsBijectiveArrow (monic ∧ epic) follows from IsIsomorphism. Concept-level || (not an is_epic_arrow_v partial spec) for the same cross-module-firing reason as IsMonicArrow.