Theorems · Inductive type · commutative algebra

Algebra.IsPushout

(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'] → [IsScalarTower R R' S'] → [IsScalarTower R S S'] → Prop

A type-class stating that the following diagram of scalar towers `` R → S ↓ ↓ R' → S' ` is a pushout diagram (i.e. S' = S ⊗[R] R'`)

Defined in

Mathlib.RingTheory.IsTensorProduct

Cited by

59 results in Mathlib

Foundations

Depth 3 from the axioms · uses no axioms

Assumes

CommSemiringCommSemiringAlgebraCommSemiringCommSemiringAlgebraAlgebraAlgebraAlgebraIsScalarTowerIsScalarTower