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:

- Fix a category $mathcal{C}$.
- 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.
- 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.
- To each object $U$ of $mathcal{C}$ and a cover ${U_alpharightarrow U}$, one associates what is called a
*descent category*of $U$ with respect to the cover ${U_alpharightarrow U}$, usually denoted by $mathcal{D}({U_alpharightarrow U})$. It is then observed that there is an obvious way to produce a functor $mathcal{D}(U)rightarrow mathcal{D}({U_alpharightarrow U})$, where $mathcal{D}(U)$ is the “fiber category” of $U$. - 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 ${U_alpharightarrow U}$, the functor $mathcal{D}(U)rightarrow mathcal{D}({U_alpharightarrow U})$ 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:

- Fix a scheme $S$ and consider the category $text{Sch}/S$.
- Category of manifolds $text{Man}$.
- 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; Carchedi – Categorical properties of topological and differentiable stacks; Noohi – Homotopy types of topological stacks; Metzler – Topological and smooth stacks) 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)?