Theorems · Theorem · linear algebra

PiTensorProduct.equivPiTensorComplSingletonTensor_symm_tmul

∀ (R : Type u_1) {ι : Type u_2} [inst : DecidableEq ι] (M : ι → Type u_3) [inst_1 : CommSemiring R]
  [inst_2 : (i : ι) → AddCommMonoid (M i)] [inst_3 : (i : ι) → Module R (M i)] (i₀ : ι)
  (m : (i : ↑(Set.singleton i₀)ᶜ) → M ↑i) (x : M i₀),
  (PiTensorProduct.equivPiTensorComplSingletonTensor R M i₀).symm (((PiTensorProduct.tprod R) fun j => m j) ⊗ₜ[R] x) =
    ⨂ₜ[R] (i : ι), Function.subtypeNeLift i₀ m x i

Defined in

Mathlib.LinearAlgebra.PiTensorProduct.Generators

Cited by

0 results in Mathlib

Foundations

Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DecidableEqCommSemiringAddCommMonoidModule