Theorems · Definition · ring theory

Algebra.TensorProduct.opAlgEquiv

(R : Type u_1) →
  (S : Type u_2) →
    (A : Type u_3) →
      (B : Type u_4) →
        [inst : CommSemiring R] →
          [inst_1 : CommSemiring S] →
            [inst_2 : Semiring A] →
              [inst_3 : Semiring B] →
                [inst_4 : Algebra R S] →
                  [inst_5 : Algebra R A] →
                    [inst_6 : Algebra R B] →
                      [inst_7 : Algebra S A] →
                        [inst_8 : IsScalarTower R S A] → TensorProduct R Aᵐᵒᵖ Bᵐᵒᵖ ≃ₐ[S] (TensorProduct R A B)ᵐᵒᵖ

MulOpposite distributes over TensorProduct. Note this is an S-algebra morphism, where A/S/R is a tower of algebras.

Defined in

Mathlib.LinearAlgebra.TensorProduct.Opposite

Cited by

6 results in Mathlib

Foundations

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

Assumes

CommSemiringCommSemiringSemiringSemiringAlgebraAlgebraAlgebraAlgebraIsScalarTower