Theorems · Definition · ring theory

Algebra.TensorProduct.congr

{R : Type uR} →
  {S : Type uS} →
    {A : Type uA} →
      {B : Type uB} →
        {C : Type uC} →
          {D : Type uD} →
            [inst : CommSemiring R] →
              [inst_1 : CommSemiring S] →
                [inst_2 : Algebra R S] →
                  [inst_3 : Semiring A] →
                    [inst_4 : Algebra R A] →
                      [inst_5 : Algebra S A] →
                        [inst_6 : IsScalarTower R S A] →
                          [inst_7 : Semiring B] →
                            [inst_8 : Algebra R B] →
                              [inst_9 : Semiring C] →
                                [inst_10 : Algebra R C] →
                                  [inst_11 : Algebra S C] →
                                    [inst_12 : IsScalarTower R S C] →
                                      [inst_13 : Semiring D] →
                                        [inst_14 : Algebra R D] →
                                          (A ≃ₐ[S] C) → (B ≃ₐ[R] D) → TensorProduct R A B ≃ₐ[S] TensorProduct R C D

Construct an isomorphism between tensor products of an S-algebra with an R-algebra from S- and R- isomorphisms between the tensor factors.

Defined in

Mathlib.RingTheory.TensorProduct.Maps

Cited by

26 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringCommSemiringAlgebraSemiringAlgebraAlgebraIsScalarTowerSemiringAlgebraSemiringAlgebraAlgebraIsScalarTowerSemiringAlgebra