Terminal object

Definition
An object $S$ in a category $\mathcal{C}$ is a terminal object of $\mathcal{C}$ if for each object $X$ of $\mathcal{C}$ there exists exactly one $\mathcal{C}$-map $X\to S$.
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It can be shown that if $S_1$ and $S_2$ are two terminal objects they are, essentially, the same since there exists one $\mathcal{C}$-map

which is, also, an isomorphism (@lawvere2009conceptual page 226).