Theorems · Theorem · linear algebra

PiTensorProduct.ofFinsuppEquiv_apply

∀ {R : Type u_1} {ι : Type u_2} {κ : ι → Type u_3} {M : ι → Type u_4} [inst : CommSemiring R] [inst_1 : Fintype ι]
  [inst_2 : DecidableEq ι] [inst_3 : (i : ι) → DecidableEq (κ i)] [inst_4 : (i : ι) → AddCommMonoid (M i)]
  [inst_5 : (i : ι) → Module R (M i)] [inst_6 : (i : ι) → DecidableEq (M i)] (f : (i : ι) → κ i →₀ M i)
  (p : (i : ι) → κ i),
  (PiTensorProduct.ofFinsuppEquiv ((PiTensorProduct.tprod R) fun i => f i)) p = ⨂ₜ[R] (i : ι), (f i) (p i)

Defined in

Mathlib.LinearAlgebra.PiTensorProduct.Finsupp

Cited by

2 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringFintypeDecidableEqDecidableEqAddCommMonoidModuleDecidableEq