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Theorems · Theorem · ring theory

AlgHom.pi_comp

∀ {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)] {B : Type u_4} {C : Type u_5} [inst_3 : Semiring B] [inst_4 : Algebra R B]
  [inst_5 : Semiring C] [inst_6 : Algebra R C] (g : (i : ι) → C →ₐ[R] A i) (h : B →ₐ[R] C),
  (AlgHom.pi g).comp h = AlgHom.pi fun i => (g i).comp h

AlgHom.pi commutes with composition.

Defined in
Mathlib.Algebra.Algebra.Pi
Cited by
1 results in Mathlib
Foundations
Depth 24 from the axioms · uses propext, Quot.sound
Assumes
CommSemiringSemiringAlgebraSemiringAlgebraSemiringAlgebra
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Polynomial.aeval_pi · cited by 1Polynomial.aeval_piSemiring · cited by 13802SemiringAlgebra · cited by 11388AlgebraCommSemiring · cited by 10911CommSemiringAlgHom · cited by 3236AlgHomAlgHom.comp · cited by 501AlgHom.compAlgHom.pi · cited by 9AlgHom.piAlgHom.pi_compCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.