Terminal object

Definition

A terminal object in a category $𝐂$ is an object $1\in 𝐂$ such that there exists precisely one morphism $!:x\to 1$ for every $𝐂$-object $x$.

Examples

• If a category $𝐂$ has a terminal object $t$, its identity morphism \id{t} ParseError: Unexpected end of input in a macro argument, expected '}' at end of input: \id{t} is a terminal object in the arrow category $\text{ArrowCategory}𝐂$.

References

• [cite:@enwiki:1197703455]