Theorems · Theorem · linear algebra

TensorProduct.lift.unique

∀ {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} {P₂ : Type u_17} [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid N] [inst_4 : AddCommMonoid P₂]
  [inst_5 : Module R M] [inst_6 : Module R N] [inst_7 : Module R₂ P₂] {f' : M →ₛₗ[σ₁₂] N →ₛₗ[σ₁₂] P₂}
  {g : TensorProduct R M N →ₛₗ[σ₁₂] P₂}, (∀ (x : M) (y : N), g (x ⊗ₜ[R] y) = (f' x) y) → g = TensorProduct.lift f'

Defined in

Mathlib.LinearAlgebra.TensorProduct.Basic

Cited by

3 results in Mathlib

Foundations

Depth 58 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringCommSemiringAddCommMonoidAddCommMonoidAddCommMonoidModuleModuleModule