Theorems · Theorem · linear algebra

TensorProduct.ext_fourfold

∀ {R : Type u_1} {R₂ : Type u_2} [inst : CommSemiring R] [inst_1 : CommSemiring R₂] {σ₁₂ : R →+* R₂} {M : Type u_7}
  {N : Type u_8} {P : Type u_9} {Q : Type u_10} {P₂ : Type u_17} [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid N]
  [inst_4 : AddCommMonoid P] [inst_5 : AddCommMonoid Q] [inst_6 : AddCommMonoid P₂] [inst_7 : Module R M]
  [inst_8 : Module R N] [inst_9 : Module R₂ P₂] [inst_10 : Module R P] [inst_11 : Module R Q]
  {g h : TensorProduct R (TensorProduct R (TensorProduct R M N) P) Q →ₛₗ[σ₁₂] P₂},
  (∀ (w : M) (x : N) (y : P) (z : Q), g (w ⊗ₜ[R] x ⊗ₜ[R] y ⊗ₜ[R] z) = h (w ⊗ₜ[R] x ⊗ₜ[R] y ⊗ₜ[R] z)) → g = h

Defined in

Mathlib.LinearAlgebra.TensorProduct.Basic

Cited by

2 results in Mathlib

Foundations

Depth 62 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringCommSemiringAddCommMonoidAddCommMonoidAddCommMonoidAddCommMonoidAddCommMonoidModuleModuleModuleModuleModule