Symmetric Closed Monoidal Category

A Symmetric Monoidal Category ( 𝒞 , ⊗ , I ) 𝒞 tensor-product 𝐼 (\mathcal{C},\otimes,I) is closed if for all objects X : 𝒞 : 𝑋 𝒞 X:\mathcal{C} , the tensor product functor − ⊗ X : 𝒞 → 𝒞 -\otimes X:\mathcal{C}\to\mathcal{C} has a Right Adjoint [ X , − ] : 𝒞 → 𝒞 : 𝑋 → 𝒞 𝒞 [X,-]:\mathcal{C}\to\mathcal{C} .