Let $C$ and $D$ are 2 non empty categories and $[C,D]$ is the category of functors between $C$ and $D$. I assume that the constant functor $\Delta_t$ (that maps all objects from $C$ into a single object $t$ from $D$) is the terminal object in the category. I also think that it always exists. Am I right?
Another question is about initial object in the category. What it is?