Example 4.2.2.7. Let $\operatorname{\mathcal{E}}$ be a category, let $[0]$ denote the category having a single object and a single morphism, and let $U: \operatorname{\mathcal{E}}\rightarrow [0]$ be the unique functor. The following conditions are equivalent:
The functor $U$ is a fibration in groupoids.
The functor $U$ is an opfibration in groupoids.
The category $\operatorname{\mathcal{E}}$ is a groupoid.