Theorems · Definition · commutative algebra

IsBaseChange.linearMapLeftRightHom

{R : Type u_1} →
  [inst : CommSemiring R] →
    {S : Type u_2} →
      [inst_1 : CommSemiring S] →
        [inst_2 : Algebra R S] →
          {M : Type u_3} →
            [inst_3 : AddCommMonoid M] →
              [inst_4 : Module R M] →
                {N : Type u_4} →
                  [inst_5 : AddCommMonoid N] →
                    [inst_6 : Module R N] →
                      {P : Type u_5} →
                        [inst_7 : AddCommMonoid P] →
                          [inst_8 : Module R P] →
                            {Q : Type u_6} →
                              [inst_9 : AddCommMonoid Q] →
                                [inst_10 : Module R Q] →
                                  [inst_11 : Module S P] →
                                    [inst_12 : IsScalarTower R S P] →
                                      [inst_13 : Module S Q] →
                                        [inst_14 : IsScalarTower R S Q] →
                                          {α : M →ₗ[R] P} → IsBaseChange S α → (N →ₗ[R] Q) → (M →ₗ[R] N) →ₗ[R] P →ₗ[S] Q

The base change map for linear maps with source a free finite module.

Defined in

Mathlib.RingTheory.TensorProduct.IsBaseChangeHom

Cited by

6 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringCommSemiringAlgebraAddCommMonoidModuleAddCommMonoidModuleAddCommMonoidModuleAddCommMonoidModuleModuleIsScalarTowerModuleIsScalarTower