# initial object

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## English[edit]

### Noun[edit]

**initial object** (*plural* **initial objects**)

- (category theory) An object within a category which sends out arrows to all other objects in that category, and such that each of these arrows is unique.
*In the category of sets, the***initial object**is the empty set, since there exists a unique function, namely the empty function, from the empty set into any other given set.