[[Category]]
# Objects as functors

Let $\cat C$ be a [[category]].
It is often useful to view an object $X \in \Ob \cat C$ as a [[functor]] (or [[Commutative diagram|diagram]]) from the single-object [[trivial category]] $\cat 1$, so
$$
\begin{align*}
\tilde{X} : \cat 1 &\to \cat C \\
\bullet &\mapsto X
\end{align*}
$$
See also [[objects as identities]].

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