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Currying and uncurrying is defined between functions in $Z^{X \times Y}$ (the first set) and $\left( Z^Y \right)^X$ (the second set).

But what if $Y$ is not a constant but is dependent on $X$?

The first set would become $Z^{\sum_{i\in X}Y_i}$.

What may be a proper expressing for the second set in the case of dependent $Y$?

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Does $\Sigma$ refer to the coproduct in $\mathsf{Set}$? – John Stalfos Apr 13 '12 at 16:07
@John Stalfos: Yes. – porton Apr 13 '12 at 16:16
up vote 2 down vote accepted

It seems that I found a solution myself:

the first set: $Z^{\sum_{i \in X} Y_i}$

the second set: $\prod_{i \in X} Z^{Y_i}$

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