Kerodon

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Example 2.2.3.2. Let $\operatorname{\mathcal{C}}$ be a category which admits pushouts, and let $\operatorname{Cospan}(\operatorname{\mathcal{C}})$ be the $2$-category of cospans in $\operatorname{\mathcal{C}}$ (see Example 2.2.2.1). Then the opposite $2$-category $\operatorname{Cospan}(\operatorname{\mathcal{C}})^{\operatorname{op}}$ can be identified with $\operatorname{Cospan}(\operatorname{\mathcal{C}})$ itself (every cospan from $X$ to $Y$ in $\operatorname{\mathcal{C}}$ can also be viewed as a cospan from $Y$ to $X$).