Theorems · Definition · commutative algebra

Algebra.IsPushout.equiv

(R : Type u_1) →
  (S : Type v₃) →
    [inst : CommSemiring R] →
      [inst_1 : CommSemiring S] →
        [inst_2 : Algebra R S] →
          (R' : Type u_6) →
            (S' : Type u_7) →
              [inst_3 : CommSemiring R'] →
                [inst_4 : CommSemiring S'] →
                  [inst_5 : Algebra R R'] →
                    [inst_6 : Algebra S S'] →
                      [inst_7 : Algebra R' S'] →
                        [inst_8 : Algebra R S'] →
                          [inst_9 : IsScalarTower R R' S'] →
                            [inst_10 : IsScalarTower R S S'] →
                              [h : Algebra.IsPushout R S R' S'] → TensorProduct R S R' ≃ₐ[S] S'

The isomorphism S' ≃ S ⊗[R] R given Algebra.IsPushout R S R' S'.

Defined in

Mathlib.RingTheory.IsTensorProduct

Cited by

18 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringCommSemiringAlgebraCommSemiringCommSemiringAlgebraAlgebraAlgebraAlgebraIsScalarTowerIsScalarTowerAlgebra.IsPushout