Theorems · Theorem · linear algebra

TensorProduct.assoc_tensor

∀ {R : Type u_1} [inst : CommSemiring R] {M : Type u_5} {N : Type u_6} {Q : Type u_8} {S : Type u_9}
  [inst_1 : AddCommMonoid M] [inst_2 : AddCommMonoid N] [inst_3 : AddCommMonoid Q] [inst_4 : AddCommMonoid S]
  [inst_5 : Module R M] [inst_6 : Module R N] [inst_7 : Module R Q] [inst_8 : Module R S],
  TensorProduct.assoc R (TensorProduct R M N) Q S =
    LinearEquiv.rTensor S (TensorProduct.assoc R M N Q) ≪≫ₗ TensorProduct.assoc R M (TensorProduct R N Q) S ≪≫ₗ
        LinearEquiv.lTensor M (TensorProduct.assoc R N Q S) ≪≫ₗ
      (TensorProduct.assoc R M N (TensorProduct R Q S)).symm

Defined in

Mathlib.LinearAlgebra.TensorProduct.Associator

Cited by

0 results in Mathlib

Foundations

Depth 70 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringAddCommMonoidAddCommMonoidAddCommMonoidAddCommMonoidModuleModuleModuleModule