Let $\mathscr{A}$ be a category. An object $I \in \mathscr{A}$ is initial if for every $A \in \mathscr{A}$, there is exactly one map $I \to A$. An object $T \in \mathscr{A}$ is terminal if for every $A \in \mathscr{A}$, there is exactly one map $A \to T$.