Theorems · Theorem · ring theory
AlgHom.cancel_left
∀ {R : Type u} {A : Type v} {B : Type w} {C : Type u₁} [inst : CommSemiring R] [inst_1 : Semiring A]
[inst_2 : Semiring B] [inst_3 : Semiring C] [inst_4 : Algebra R A] [inst_5 : Algebra R B] [inst_6 : Algebra R C]
{g₁ g₂ : A →ₐ[R] B} {f : B →ₐ[R] C}, Function.Injective ⇑f → (f.comp g₁ = f.comp g₂ ↔ g₁ = g₂)- Defined in
- Mathlib.Algebra.Algebra.Hom
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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.compstatement and proof · cited by 501
- AlgHom.extproof · cited by 170
- AlgHom.ext_iffproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- IsAdicComplete.algHom_extproof · cited by 0
- GradedAlgHom.cancel_leftproof · cited by 0