| 1. | Obtained by extending the identity map of the algebraic tensor product.
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| 2. | See also : tensor product of algebras, change of rings.
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| 3. | Here the tensor product is interpreted in the former sense of.
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| 4. | So complexification first and then tensor product wouldn't work.
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| 5. | Similarly, internal tensor product is left adjoint to internal Hom.
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| 6. | Its associativity follows from the associativity of the tensor product.
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| 7. | This implements the tensor product, yielding a composite tensor.
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| 8. | Recall that the derived functors of the tensor product are denoted Tor.
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| 9. | Tensor products of Hilbert spaces arise often in quantum mechanics.
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| 10. | The Hilbert space of the composite system is the tensor product
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