Terminal Object

In a Category $\mathcal{C}$, $A$ is a terminal object iff

$$\forall B:\mathcal{C}.\exists !f:B\to A.$$

Remarks

All terminal objects in $\mathcal{C}$ are initial objects in ${\mathcal{C}}^{op}$. All terminal objects are isomorphic. If an terminal object is also an initial object then it is called a zero object or a “null object”. A terminal object is an example of a limit of the empty diagram.