Theorems · Theorem · commutative algebra

Algebra.isPushout_iff

∀ (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'],
  Algebra.IsPushout R S R' S' ↔ IsBaseChange S (IsScalarTower.toAlgHom R R' S').toLinearMap

Defined in

Mathlib.RingTheory.IsTensorProduct

Cited by

5 results in Mathlib

Foundations

Depth 62 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringCommSemiringAlgebraCommSemiringCommSemiringAlgebraAlgebraAlgebraAlgebraIsScalarTowerIsScalarTower