# Azimuth Math Book Initial object

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

Example: in the category $Set$, the empty set is an initial object. Because: from empty to any other set, there is exactly one function, which is the empty function.

The empty set is also the only initial object in the category Set.