Terminal object

An object $T$ in a category $C$ is **terminal** if for every object $X$ in $C$, there exists exactly one arrow $a: X \rightarrow T$ going from $X$ to $T$.

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

See also:

- Initial object - the dual construct

category: definition, category-theory