Theorems · Definition · linear algebra

TensorProduct.piRightInv

(R : Type u_1) →
  [inst : CommSemiring R] →
    (S : Type u_2) →
      [inst_1 : CommSemiring S] →
        [inst_2 : Algebra R S] →
          (N : Type u_3) →
            [inst_3 : AddCommMonoid N] →
              [inst_4 : Module R N] →
                [inst_5 : Module S N] →
                  [inst_6 : IsScalarTower R S N] →
                    {ι : Type u_4} →
                      (M : ι → Type u_5) →
                        [inst_7 : (i : ι) → AddCommMonoid (M i)] →
                          [inst_8 : (i : ι) → Module R (M i)] →
                            [Fintype ι] →
                              [DecidableEq ι] →
                                ((i : ι) → TensorProduct R N (M i)) →ₗ[S] TensorProduct R N ((i : ι) → M i)

(Implementation): Inverse for TensorProduct.piRight.

Defined in

Mathlib.LinearAlgebra.TensorProduct.Pi

Cited by

0 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringCommSemiringAlgebraAddCommMonoidModuleModuleIsScalarTowerAddCommMonoidModuleFintypeDecidableEq