> Are there any (What are the) occurrences of the notion of "stack" outside algebraic geometry?

In most of the references, the introduction of the notion of a stack takes the following steps:

 1. Fix a category $\mathcal{C}$. 
 2. Define the notion of category fibered in groupoids/ fibered category over $\mathcal{C}$; which is simply a functor $\mathcal{D}\rightarrow \mathcal{C}$ satisfying certain conditions.
 3. Fix a Grothendieck topology on $\mathcal{C}$; this associates to each object $U$ of $\mathcal{C}$, a collection $\mathcal{J}_U$ (that is a collection of collections of arrows whose target is $U$) that are required to satisfy certain conditions.
 4. To each object $U$ of $\mathcal{C}$ and a cover $\{U_\alpha\rightarrow U\}$, one associates what is called a *descent category* of $U$ with respect to the cover $\{U_\alpha\rightarrow U\}$, usually denoted by $\mathcal{D}(\{U_\alpha\rightarrow U\})$. It is then observed that there is an obvious way to produce a functor $\mathcal{D}(U)\rightarrow \mathcal{D}(\{U_\alpha\rightarrow U\})$, where $\mathcal{D}(U)$ is the "fiber category" of $U$.
 5. A category fibered in groupoids $\mathcal{D}\rightarrow \mathcal{C}$ is then called a $\mathcal{J}$-stack (or simply a stack), if, for each object $U$ of $\mathcal{C}$ and for each cover $\{U_\alpha\rightarrow U\}$, the functor $\mathcal{D}(U)\rightarrow \mathcal{D}(\{U_\alpha\rightarrow U\})$ is an equivalence of categories.

None of the above 5 steps has anything to do with the set up of algebraic geometry. But, immediately after defining the notion of a stack, we restrict ourselves to one of the following categories, with an appropriate Grothendieck topology:

 1. Fix a scheme $S$ and consider the category $\text{Sch}/S$.
 2. Category of manifolds $\text{Man}$.
 3. Category of topological spaces $\text{Top}$.

Frequency of occurrence of stacks over above categories is in the decreasing order of magnitude. Unfortunately, I myself have seen exactly four research articles ([Noohi - Foundations of topological stacks I][1]; [Carchedi - Categorical properties of topological and differentiable stacks][2]; [Noohi - Homotopy types of topological stacks][3]; [Metzler - Topological and smooth stacks][4]) talking about stacks over the category of topological spaces. 

So, the following question arises:

> Are there any (What are the) occurrences of the notion of "stack" outside algebraic geometry (other than what I have mentioned above)? 
  
 
  [1]: https://arxiv.org/abs/math/0503247
  [2]: http://math.gmu.edu/~dcarched/Thesis_David_Carchedi.pdf
  [3]: https://arxiv.org/abs/0808.3799
  [4]: https://arxiv.org/abs/math/0306176