# Kerodon

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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.