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** Tensor product
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Tensor and product
Tensor products: If C denotes the category of vector spaces over a fixed field, with linear maps as morphisms, then the tensor product defines a functor C × C → C which is covariant in both arguments.
; Tensor product of fields: A different foundational piece of algebra, including the compositum operation ( join of fields ).
For Hilbert spaces or nuclear spaces there is a simple well-behaved theory of tensor products ( see Tensor product of Hilbert spaces ), but for general Banach spaces or locally convex topological vector space the theory is notoriously subtle.
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