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hom-set_adjunction [2016/02/11 13:22] nikolaj |
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| If ${\bf C}\neq{\bf D}$, then viewing $G$ as indexing may be harder. | If ${\bf C}\neq{\bf D}$, then viewing $G$ as indexing may be harder. | ||
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| - | == Example from Algebra == | ||
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| - | For example in the category of groups | ||
| - | |||
| - | $\mathrm{Hom}(X\otimes A,Y)\cong\mathrm{Hom}(X,\mathrm{Hom}(A,Y))$ | ||
| == Currying == | == Currying == | ||
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| Here the A-"thickening" side says you have more arugments to prove $Y$ to begin with, while the $A$-"indexing" side means you only demonstrate A-conditional truth of $Y$. | Here the A-"thickening" side says you have more arugments to prove $Y$ to begin with, while the $A$-"indexing" side means you only demonstrate A-conditional truth of $Y$. | ||
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| + | == Example from Algebra == | ||
| + | |||
| + | For example in the category of groups | ||
| + | |||
| + | $\mathrm{Hom}(X\otimes A,Y)\cong\mathrm{Hom}(X,\mathrm{Hom}(A,Y))$ | ||
| == Galois connection == | == Galois connection == | ||
