Theorems · Definition · commutative algebra

IsBaseChange.lift

{R : Type u_1} →
  {M : Type v₁} →
    {N : Type v₂} →
      {S : Type v₃} →
        [inst : AddCommMonoid M] →
          [inst_1 : AddCommMonoid N] →
            [inst_2 : CommSemiring R] →
              [inst_3 : CommSemiring S] →
                [inst_4 : Algebra R S] →
                  [inst_5 : Module R M] →
                    [inst_6 : Module R N] →
                      [inst_7 : Module S N] →
                        [inst_8 : IsScalarTower R S N] →
                          {f : M →ₗ[R] N} →
                            IsBaseChange S f →
                              {Q : Type u_3} →
                                [inst_9 : AddCommMonoid Q] →
                                  [inst_10 : Module S Q] →
                                    [inst_11 : Module R Q] → [IsScalarTower R S Q] → (M →ₗ[R] Q) → N →ₗ[S] Q

Suppose f : M →ₗ[R] N is the base change of M along R → S. Then any R-linear map from M to an S-module factors through f.

Defined in

Mathlib.RingTheory.IsTensorProduct

Cited by

6 results in Mathlib

Foundations

Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidAddCommMonoidCommSemiringCommSemiringAlgebraModuleModuleModuleIsScalarTowerAddCommMonoidModuleModuleIsScalarTower