## Terminal object

### Object

context | ${\bf C}$ … category |

definiendum | $T$ |

inclusion | $T:\mathrm{Ob}_{\bf C}$ |

for all | $X:\mathrm{Ob}_{\bf C}$ |

postulate | $\exists!i.\ i:{\bf C}[X,T]$ |

### Discussion

See Initial object for the definition of the dual, as well as a characterization as universal morphism.

#### Reference

Wikipedia: Initial and terminal objects