Theorems · Theorem · commutative algebra

Algebra.IsPushout.of_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 R' S S'] {T : Type u_8} [inst_11 : CommSemiring T] [inst_12 : Algebra R' T]
  [inst_13 : Algebra S T] [inst_14 : Algebra R T] [inst_15 : IsScalarTower R S T] [inst_16 : IsScalarTower R R' T]
  (e : S' ≃ₐ[R'] T), e.toRingEquiv.toRingHom.comp (algebraMap S S') = algebraMap S T → Algebra.IsPushout R R' S T

Defined in

Mathlib.RingTheory.IsTensorProduct

Cited by

1 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringCommSemiringAlgebraCommSemiringCommSemiringAlgebraAlgebraAlgebraAlgebraIsScalarTowerIsScalarTowerAlgebra.IsPushoutCommSemiringAlgebraAlgebraAlgebraIsScalarTowerIsScalarTower