Theorems · Definition · linear algebra

PiTensorProduct.map

{ι : Type u_1} →
  {R : Type u_4} →
    [inst : CommSemiring R] →
      {s : ι → Type u_7} →
        [inst_1 : (i : ι) → AddCommMonoid (s i)] →
          [inst_2 : (i : ι) → Module R (s i)] →
            {t : ι → Type u_11} →
              [inst_3 : (i : ι) → AddCommMonoid (t i)] →
                [inst_4 : (i : ι) → Module R (t i)] →
                  ((i : ι) → s i →ₗ[R] t i) → (PiTensorProduct R fun i => s i) →ₗ[R] PiTensorProduct R fun i => t i

Let sᵢ and tᵢ be two families of R-modules. Let f be a family of R-linear maps between sᵢ and tᵢ, i.e. f : Πᵢ sᵢ → tᵢ, then there is an induced map ⨂ᵢ sᵢ → ⨂ᵢ tᵢ by ⨂ aᵢ ↦ ⨂ fᵢ aᵢ. This is TensorProduct.map for an arbitrary family of modules.

Defined in

Mathlib.LinearAlgebra.PiTensorProduct.Basic

Cited by

24 results in Mathlib

Foundations

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

Assumes

CommSemiringAddCommMonoidModuleAddCommMonoidModule