Theorems · Definition · commutative algebra

Algebra.Generators.baseChangeFromBaseChange

{R : Type u} →
  {S : Type v} →
    {ι : Type w} →
      [inst : CommRing R] →
        [inst_1 : CommRing S] →
          [inst_2 : Algebra R S] →
            (P : Algebra.Generators R S ι) →
              (T : Type u_2) →
                [inst_3 : CommRing T] →
                  [inst_4 : Algebra R T] → P.toExtension.baseChange.Hom (Algebra.Generators.baseChange T P).toExtension

The forwards direction of the canonical isomorphism T ⊗[R] R[Xᵢ] ≃ₐ[T] T[Xᵢ] as a map of extensions.

Defined in

Mathlib.RingTheory.Extension.Generators

Cited by

2 results in Mathlib

Foundations

Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraCommRingAlgebra