Theorems · Definition · linear algebra

TensorProduct.curry

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

Given a semilinear map M ⊗ N → P, compose it with the canonical bilinear map M → N → M ⊗ N to form a bilinear map M → N → P.

Defined in

Mathlib.LinearAlgebra.TensorProduct.Basic

Cited by

28 results in Mathlib

Foundations

Depth 67 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringCommSemiringAddCommMonoidAddCommMonoidAddCommMonoidModuleModuleModule