Theorems · Definition · linear algebra

PiTensorProduct.subsingletonEquiv

{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)] →
            [Subsingleton ι] → (i₀ : ι) → (PiTensorProduct R fun i => s i) ≃ₗ[R] s i₀

Tensor product over a singleton type with element i₀ is equivalent to s i₀.

Defined in

Mathlib.LinearAlgebra.PiTensorProduct.Basic

Cited by

6 results in Mathlib

Foundations

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

Assumes

CommSemiringAddCommMonoidModuleSubsingleton