Talk:Category of sets

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[edit] Nullary intersection

Here is a beginner question that should be addressed: notable in its absence is any mention of the idea of intersection of sets. I presume that this is intentional, and due to the problem of the nullary intersection. This should be belaboured.

In a related sense, the empty set cannot be a terminal object; I think this point could be belaboured. That is, the reason that the empty set cannot be terminal is because there do not exist any functions that do not map anything: a tautologically vacous truth. This should not be confused with the case of a function that maps all the elements of a set to the empty set: such a function does exist, and it is an example of a morphism to a singleton: in this case, the singleeton is the set containing the empty set. Similarly, all singletons are terminal objects.

A discussion along these lines would benefit the article, but I'm not feeling bold enough to do this myself. linas 01:24, 21 July 2006 (UTC)