If $T$ is terminal object, is also $\text{hom}(X,T)$ a terminal object? In a category with internal Hom and terminal object $T$. Is it true that also $\text{hom}(X,T)$ is a terminal object for any object $X$?
It is definitely true for $\mathbf{Set}$ or $\mathbf{Vec}$, but I'm not sure  if it is true in general.
I'm probably stuck in thinking about sets, and I do not even know where to start in proving or disproving it.

By definition of the terminal object, $\hom(X,T)$ is a one element set for every $X$.
And one element sets are exactly the terminal objects in $Set$. 
