Theorems · Theorem · commutative algebra

Algebra.IsPushout.cancelBaseChange_symm_comp_lTensor

∀ (R : Type u_1) [inst : CommSemiring R] (A : Type u_8) [inst_1 : CommRing A] [inst_2 : Algebra R A] (C : Type u_11)
  [inst_3 : CommRing C] [inst_4 : Algebra R C] [inst_5 : Algebra A C] [inst_6 : IsScalarTower R A C] (S : Type u_12)
  [inst_7 : CommRing S] [inst_8 : Algebra R S],
  (↑(Algebra.IsPushout.cancelBaseChangeAlg R S A (TensorProduct R S A) C).symm).comp
      (Algebra.TensorProduct.lTensor S (IsScalarTower.toAlgHom R A C)) =
    Algebra.TensorProduct.includeLeft

Defined in

Mathlib.RingTheory.IsTensorProduct

Cited by

1 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringCommRingAlgebraCommRingAlgebraAlgebraIsScalarTowerCommRingAlgebra