Theorems · Theorem · commutative algebra

Algebra.IsPushout.algHom_ext

∀ {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'] {A : Type u_8} [inst_11 : Semiring A] [inst_12 : Algebra R A] {f g : S' →ₐ[R] A},
  f.comp (IsScalarTower.toAlgHom R R' S') = g.comp (IsScalarTower.toAlgHom R R' S') →
    f.comp (IsScalarTower.toAlgHom R S S') = g.comp (IsScalarTower.toAlgHom R S S') → f = g

Defined in

Mathlib.RingTheory.IsTensorProduct

Cited by

0 results in Mathlib

Foundations

Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringCommSemiringAlgebraCommSemiringCommSemiringAlgebraAlgebraAlgebraAlgebraIsScalarTowerIsScalarTowerAlgebra.IsPushoutSemiringAlgebra