Theorems · Definition · linear algebra

TensorProduct.lift

{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] → (M →ₛₗ[σ₁₂] N →ₛₗ[σ₁₂] P₂) → TensorProduct R M N →ₛₗ[σ₁₂] P₂

Constructing a linear map M ⊗ N → P given a bilinear map M → N → P with the property that its composition with the canonical bilinear map M → N → M ⊗ N is the given bilinear map M → N → P. This works for semilinear maps.

Defined in

Mathlib.LinearAlgebra.TensorProduct.Basic

Cited by

59 results in Mathlib

Foundations

Depth 56 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringCommSemiringAddCommMonoidAddCommMonoidAddCommMonoidModuleModuleModule