Theorems · Definition · ring theory
AlgHom.equalizer
{R : Type u_1} →
{A : Type u_2} →
{B : Type u_3} →
[inst : CommSemiring R] →
[inst_1 : Semiring A] →
[inst_2 : Algebra R A] →
[inst_3 : Semiring B] → [inst_4 : Algebra R B] → (A →ₐ[R] B) → (A →ₐ[R] B) → Subalgebra R AThe equalizer of two R-algebra homomorphisms
- Defined in
- Mathlib.Algebra.Algebra.Subalgebra.Basic
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · 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
- Set.ofPredproof · cited by 6,101
- AlgHomstatement and proof · cited by 3,236
- Subalgebrastatement · cited by 1,353
Cited by30
Results whose statement or proof uses this declaration.
- RingHom.HasEqualizersproof · cited by 6
- Polynomial.Gal.extproof · cited by 5
- AlgHom.pullbackproof · cited by 5
- StarAlgHom.equalizerproof · cited by 4
- AlgHom.tensorEqualizerstatement · cited by 3
- CommRingCat.Under.equalizerForkproof · cited by 3
- AlgHom.adjoin_le_equalizerstatement · cited by 2
- AlgHom.eqOn_adjoin_iffproof · cited by 2
- AlgHom.tensorEqualizerAuxstatement · cited by 1
- AlgHom.tensorEqualizerEquivstatement · cited by 1
- CommRingCat.Under.equalizerFork'proof · cited by 1
- CommRingCat.preservesLimit_parallelPair_tensorProd_iff_tensorEqualizer_bijectivestatement and proof · cited by 1