The Stacks project

Remark 89.21.2. A groupoid in functors on $\mathcal{C}$ amounts to the data of a functor $\mathcal{C} \to \textit{Groupoids}$, and a morphism of groupoids in functors on $\mathcal{C}$ amounts to a morphism of the corresponding functors $\mathcal{C} \to \textit{Groupoids}$ (where $\textit{Groupoids}$ is regarded as a 1-category). However, for our purposes it is more convenient to use the terminology of groupoids in functors. In fact, thinking of a groupoid in functors as the corresponding functor $\mathcal{C} \to \textit{Groupoids}$, or equivalently as the category cofibered in groupoids associated to that functor, can lead to confusion (Remark 89.23.2).

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