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The dual notion of an initial object is that of a terminal object (also called terminal element):
T is a terminal object, if for every object X in ๐ฎ there exists exactly one morphism X โ T.
Terminal objects are also called final objects.
If an object is both initial and terminal, it is called a zero object or null object. A pointed category is one with a zero object.
A is the terminal object:
every singleton set is a terminal object in the category Set
there are no zero objects in the category Set