Azimuth Math Book
Initial object

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

Example: in the category SetSet, 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.

See also: