| 11. | In homological algebra, the adjointness of curry and apply is known as tensor-hom adjunction.
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| 12. | As a result, there is no right adjunction, and hence in practice no rightward movement either.
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| 13. | The monad theory matters as part of the effort to capture what it is that adjunctions'preserve '.
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| 14. | The adjunction between topological spaces and locales restricts to an equivalence of categories between sober spaces and spatial locales.
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| 15. | This shows that any adjunction of a finite set can be reduced to a successive adjunction of single elements.
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| 16. | This shows that any adjunction of a finite set can be reduced to a successive adjunction of single elements.
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| 17. | This is formally the tensor-hom adjunction, and is an archetypal example of a pair of adjoint functors.
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| 18. | Because of this adjunction, there is an associated monad on the category of sheaves on " X ".
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| 19. | More generally, it has been shown that vectorization is a self-adjunction in the monoidal closed structure of any category of matrices.
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| 20. | However, the adjoint functors " F " and " G " alone are in general not sufficient to determine the adjunction.
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