Theorems · Definition · commutative algebra

AlgEquiv.restrictScalars

(R : Type u) →
  {S : Type v} →
    {A : Type w} →
      {B : Type u₁} →
        [inst : CommSemiring R] →
          [inst_1 : CommSemiring S] →
            [inst_2 : Semiring A] →
              [inst_3 : Semiring B] →
                [inst_4 : Algebra R S] →
                  [inst_5 : Algebra S A] →
                    [inst_6 : Algebra S B] →
                      [inst_7 : Algebra R A] →
                        [inst_8 : Algebra R B] → [IsScalarTower R S A] → [IsScalarTower R S B] → (A ≃ₐ[S] B) → A ≃ₐ[R] B

R ⟶ S induces S-Alg ⥤ R-Alg

Defined in

Mathlib.Algebra.Algebra.Tower

Cited by

60 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringCommSemiringSemiringSemiringAlgebraAlgebraAlgebraAlgebraAlgebraIsScalarTowerIsScalarTower