[[Category]]
# Opposite category

Let $\cat C$ be a [[category]].
The **opposite category** $\op{\cat C}$ is the category with the same objects as $\cat C$ but whose morphisms have the domain and codomain swapped, #m/def/cat 
i.e.
$$
\begin{align*}
f \in \cat C(X,Y) \iff f \in \op{\cat C} (Y,X)
\end{align*}
$$


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