Theorems · Theorem · linear algebra

PiTensorProduct.map_reindex

∀ {ι : Type u_1} {ι₂ : Type u_2} {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)] (f : (i : ι) → s i →ₗ[R] t i)
  (e : ι ≃ ι₂) (x : PiTensorProduct R fun i => s i),
  (PiTensorProduct.map fun i => f (e.symm i)) ((PiTensorProduct.reindex R s e) x) =
    (PiTensorProduct.reindex R t e) ((PiTensorProduct.map f) x)

Defined in

Mathlib.LinearAlgebra.PiTensorProduct.Basic

Cited by

0 results in Mathlib

Foundations

Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleAddCommMonoidModule