Applications of double categories

Much of modern pure mathematics deals with abstract structures. This is useful as it allows one to see how different theories are similar while emphasizing their differences. There are many different such abstract structures and the study of how they inter-relate is the domain of category theory. Within category theory itself, there is a variety of meta structures, and it is the study of their properties that is the object of our research, namely double category theory. Thus we can imagine the whole structure of mathematics as a tree with double categories at the root, categories the next level up, then abstract structures with the final level being applications. Thus our research is foundational in nature.