Theorems · Definition · commutative algebra

Algebra.IsPushout.casesOn

{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'] →
                              {motive : Algebra.IsPushout R S R' S' → Sort u} →
                                (t : Algebra.IsPushout R S R' S') →
                                  ((out : IsBaseChange S (IsScalarTower.toAlgHom R R' S').toLinearMap) → motive ⋯) →
                                    motive t

Defined in

Mathlib.RingTheory.IsTensorProduct

Cited by

1 results in Mathlib

Foundations

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

Assumes

CommSemiringCommSemiringAlgebraCommSemiringCommSemiringAlgebraAlgebraAlgebraAlgebraIsScalarTowerIsScalarTower