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According to the book 'Categories for the Working Mathematician' (p20), the empty set is an initial object and any one-point set is a terminal object for the category 'Set'.

My question is,

"Why an empty set cannot be the terminal object for the category 'Set' as well?".

Is this because there is no isomorphism between one-point set and empty set, so we just discard empty set as a terminal object for the category 'Set'?

Thanks in advance.

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# An initial and terminal object of the category 'Set'

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