The homomorphism law of a map F on the carrier T, declared: \(f(a \odot b) = f(a) \circledast f(b)\), Op on T and Op2 on the codomain, a homomorphism of magmas (Bourbaki, Algebra I, §I.1.1); for a unary operation, \(f(u(a)) =
u'(f(a))\). A certificate, false where none is declared: the law is an equation on every pair, so it is declared and witnessed by computation at the declaration, as is_monic_arrow_v. A class template, so that a family of maps declares it once across modules; keyed like is_involutive<F, T>, a bare callable naming its carrier.
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Detailed Description
struct dedekind::category::is_homomorphism< F, T, Op, Op2 >
The homomorphism law of a map F on the carrier T, declared: \(f(a \odot b) = f(a) \circledast f(b)\), Op on T and Op2 on the codomain, a homomorphism of magmas (Bourbaki, Algebra I, §I.1.1); for a unary operation, \(f(u(a)) =
u'(f(a))\). A certificate, false where none is declared: the law is an equation on every pair, so it is declared and witnessed by computation at the declaration, as is_monic_arrow_v. A class template, so that a family of maps declares it once across modules; keyed like is_involutive<F, T>, a bare callable naming its carrier.
- Template Parameters
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F the map. T its carrier. Op the operation on T.Op2 the operation on the codomain.
The documentation for this struct was generated from the following file:
- src/main/modules/dedekind/category/morphism.cppm
