English
Equality between AlgHom from product and product of AlgHoms holds: AlgHom(coe of f₁.prod f₂) = (AlgHom f₁) . prod (AlgHom f₂).
Русский
Равенство между гомоморфизмами от произведения и произведением гомоморфизмов сохраняется.
LaTeX
$$AlgHomClass.toAlgHom (f₁.prod f₂) = (AlgHomClass.toAlgHom f₁).prod (AlgHomClass.toAlgHom f₂)$$
Lean4
instance {D : Type*} [UniformSpace D] [CompleteSpace D] [Semiring D] [Algebra R D] [T2Space B] [FunLike F D B]
[AlgHomClass F R D B] [ContinuousMapClass F D B] (f g : F) : CompleteSpace (AlgHom.equalizer f g) :=
isClosed_eq (map_continuous f) (map_continuous g) |>.completeSpace_coe
