Theorems · Theorem · ring theory
AlgHom.adjoin_le_equalizer
∀ {R : Type uR} {A : Type uA} {B : Type uB} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Semiring B]
[inst_3 : Algebra R A] [inst_4 : Algebra R B] (φ₁ φ₂ : A →ₐ[R] B) {s : Set A},
Set.EqOn (⇑φ₁) (⇑φ₂) s → Algebra.adjoin R s ≤ φ₁.equalizer φ₂- Cited by
- 2 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- AlgHomstatement and proof · cited by 3,236
- Subalgebrastatement · cited by 1,353
- Set.EqOnstatement and proof · cited by 603
- Algebra.adjoinstatement · cited by 535
- Algebra.adjoin_leproof · cited by 36
- AlgHom.equalizerstatement · cited by 21
Cited by2
Results whose statement or proof uses this declaration.
- AlgHom.ext_of_adjoin_eq_topproof · cited by 2
- polynomialFunctions.le_equalizerproof · cited by 1