Theorems · Definition · ring theory
Bialgebra.Quotient.counitAlgHom
{R : Type u_1} →
{A : Type u_2} →
[inst : CommRing R] →
[inst_1 : Ring A] →
[inst_2 : Bialgebra R A] →
(I : Ideal A) → [inst_3 : I.IsTwoSided] → [(Submodule.restrictScalars R I).IsCoideal] → A ⧸ I →ₐ[R] RThe counit on A ⧸ I, as an R-algebra homomorphism.
- Defined in
- Mathlib.RingTheory.Bialgebra.Quotient
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 87 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.
- CommRingstatement and proof · cited by 17,173
- Ringstatement and proof · cited by 7,463
- Idealstatement and proof · cited by 4,748
- AlgHomstatement · cited by 3,236
- HasQuotient.Quotientstatement · cited by 2,301
- Submodule.restrictScalarsstatement and proof · cited by 180
- Ideal.IsTwoSidedstatement and proof · cited by 179
- Bialgebrastatement and proof · cited by 160
- Bialgebra.counitAlgHomproof · cited by 23
- Submodule.IsCoidealstatement and proof · cited by 17
- Ideal.Quotient.liftₐproof · cited by 15
Cited by2
Results whose statement or proof uses this declaration.
- Bialgebra.Quotient.counit_comp_mkₐstatement · cited by 0
- Bialgebra.Quotient.counitAlgHom.congr_simpstatement and proof · cited by 0