Theorems · Theorem · commutative algebra

TensorProduct.toDirectLimit_tmul_of

∀ {R : Type u_1} [inst : CommSemiring R] {ι : Type u_2} [inst_1 : DecidableEq ι] [inst_2 : Preorder ι]
  {G : ι → Type u_3} [inst_3 : (i : ι) → AddCommMonoid (G i)] [inst_4 : (i : ι) → Module R (G i)]
  (f : (i j : ι) → i ≤ j → G i →ₗ[R] G j) {M : Type u_4} [inst_5 : AddCommMonoid M] [inst_6 : Module R M] {i : ι}
  (g : G i) (m : M),
  (TensorProduct.toDirectLimit f M) ((Module.DirectLimit.of R ι G f i) g ⊗ₜ[R] m) =
    (Module.DirectLimit.of R ι (fun x => TensorProduct R (G x) M) (fun i j h => LinearMap.rTensor M (f i j h)) i)
      (g ⊗ₜ[R] m)

Defined in

Mathlib.LinearAlgebra.TensorProduct.DirectLimit

Cited by

1 results in Mathlib

Foundations

Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringDecidableEqPreorderAddCommMonoidModuleAddCommMonoidModule