Theorems · Definition · ring theory
Pi.evalAlgHom
{ι : Type u_1} →
(R : Type u_2) →
(A : ι → Type u_3) →
[inst : CommSemiring R] →
[inst_1 : (i : ι) → Semiring (A i)] → [inst_2 : (i : ι) → Algebra R (A i)] → (i : ι) → ((i : ι) → A i) →ₐ[R] A iFunction.eval as an AlgHom. The name matches Pi.evalRingHom, Pi.evalMonoidHom,
etc.
- Defined in
- Mathlib.Algebra.Algebra.Pi
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Quot.sound
- Assumes
- CommSemiringSemiringAlgebra
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.
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomproof · cited by 10,189
- AlgHomstatement · cited by 3,236
- Pi.evalRingHomproof · cited by 44
Cited by18
Results whose statement or proof uses this declaration.
- Pi.evalAlgHom_applystatement and proof · cited by 4
- PrimeSpectrum.piLocalizationToMaximalproof · cited by 3
- CommAlgCat.FiniteEtale.equivOfIsSepClosedproof · cited by 3
- TannakaDuality.FiniteGroup.toRightFDRepComp_in_rightRegularproof · cited by 1
- LocallyConstant.evalₐproof · cited by 1
- AlgHom.pi_evalAlgHomstatement · cited by 1
- AlgHom.eq_piEvalAlgHomstatement and proof · cited by 1
- Algebra.FormallyUnramified.pi_iffproof · cited by 1
- Polynomial.aeval_piproof · cited by 1
- Algebra.FormallySmooth.pi_iffproof · cited by 1
- Algebra.FormallySmooth.of_piproof · cited by 1
- Pi.coe_evalAlgHomstatement · cited by 0