Azimuth Math Book
Terminal object

An object TT in a category CC is terminal if for every object XX in CC, there exists exactly one arrow a:XTa: X \rightarrow T going from XX to TT.

Example: in the category SetSet, the any singleton set {x}\lbrace x \rbrace is a terminal object object. Because: from any set to a singleton set {x}\lbrace x \rbrace, there is exactly one function – the constant function which maps everything to xx.

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