Theorems · Theorem · ring theory
AlgHom.ext_iff
∀ {R : Type u} {A : Type v} {B : Type w} [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}, φ₁ = φ₂ ↔ ∀ (x : A), φ₁ x = φ₂ x- Defined in
- Mathlib.Algebra.Algebra.Hom
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- 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
- AlgHom.extproof · cited by 170
Cited by5
Results whose statement or proof uses this declaration.
- AlgHom.cancel_leftproof · cited by 2
- AlgHom.cancel_rightproof · cited by 2
- IsLocalization.algHom_extproof · cited by 2
- MulSemiringAction.toAlgHom_injectiveproof · cited by 2
- KaehlerDifferential.End_equiv_auxproof · cited by 0