Question:

What are (some of) the stacks (occurring in algebraic/differential geometry) that are fibered in arbitrary categories and not necessarily in groupoids?

In the notes Notes on Grothendieck topologies,fibered categories and descent theory Angelo Vistoli introduce the notion of a stack over a site $(\mathcal{C},\mathcal{J})$ to be a fibered category (not necessarily fibered in groupoids) over $\mathcal{C}$ satisfying some "locally determined" condition.

But, examples of stacks of interest in algebraic geometry and differential geometry (a small set of examples I have seen) are always fibered in groupoids. So, what could be a justification or necessity for introducing the notion of stacks fibered over arbitrary categories, if "almost all" stacks that occur in Algebraic geometry (that I know) are fibered in groupoids.

There might be interesting examples of stacks outside algebraic geometry of differential geometry that are not necessarily fibered in groupoids. I would be happy to see such examples (please add them as answers if you wish) but as for this question, I would like to learn about situations in algebraic geometry or differential geometry.