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

In most of the references, 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 for each object $U$ of $\mathcal{C}$, a collection $\mathcal{J}_U$ (that is a collection of collection of arrows whose target is $U$) that are required to satisfy certain conditions.
 4. For 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 our self to one of the following categories:

 1. Fix a scheme $S$ and consider the category $\text{Sch}/S$, and an appropriate Grothendieck topology on $\text{Sch}/S$.
 2. Category of manifold $\text{Man}$ and an appropriate Grothendieck topology on $\text{Man}$.
 3. Category of topological spaces $\text{Top}$, and an appropriate Grothendieck topology on $\text{Top}$.

Frequency of occurrence of stacks over above categories is in the decreasing order of magnitude. Unfortunately, I myself has seen [exactly][1] [four][2] [research][3] [articles][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/pdf/math/0503247.pdf
  [2]: http://math.gmu.edu/~dcarched/Thesis_David_Carchedi.pdf
  [3]: https://arxiv.org/pdf/0808.3799.pdf
  [4]: https://arxiv.org/pdf/math/0306176.pdf