The Stacks project

Definition 90.6.2. A predeformation category $\mathcal{F}$ is a category cofibered in groupoids over $\mathcal{C}_\Lambda $ such that $\mathcal{F}(k)$ is equivalent to a category with a single object and a single morphism, i.e., $\mathcal{F}(k)$ contains at least one object and there is a unique morphism between any two objects. A morphism of predeformation categories is a morphism of categories cofibered in groupoids over $\mathcal{C}_\Lambda $.