Theorems · Definition · ring theory

AlgHom.pi

{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} →
              [inst_3 : Semiring B] → [inst_4 : Algebra R B] → ((i : ι) → B →ₐ[R] A i) → B →ₐ[R] (i : ι) → A i

A family of algebra homomorphisms g i : B →ₐ[R] A i defines an algebra homomorphism AlgHom.pi g : B →ₐ[R] Π i, A i given by AlgHom.pi g x i = g i x.

Defined in

Mathlib.Algebra.Algebra.Pi

Cited by

9 results in Mathlib

Foundations

Depth 23 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringSemiringAlgebraSemiringAlgebra