Theorems · Theorem · ring theory

StarAlgHom.adjoin_le_equalizer

∀ {F : Type u_1} {R : Type u_2} {A : Type u_3} {B : Type u_4} [inst : CommSemiring R] [inst_1 : StarRing R]
  [inst_2 : Semiring A] [inst_3 : Algebra R A] [inst_4 : StarRing A] [inst_5 : Semiring B] [inst_6 : Algebra R B]
  [inst_7 : StarRing B] [inst_8 : StarModule R A] [inst_9 : FunLike F A B] [inst_10 : AlgHomClass F R A B]
  [inst_11 : StarHomClass F A B] (f g : F) {s : Set A},
  Set.EqOn (⇑f) (⇑g) s → StarAlgebra.adjoin R s ≤ StarAlgHom.equalizer f g

Defined in

Mathlib.Algebra.Star.Subalgebra

Cited by

2 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringStarRingSemiringAlgebraStarRingSemiringAlgebraStarRingStarModuleFunLikeAlgHomClassStarHomClass