Double groupoid

Okay kiddo, imagine you have a toy car and a toy train. They're both toys, but they're different kinds of toys. Now, imagine you have two groups of toys: one group has a bunch of toy cars, and the other group has a bunch of toy trains. These are also different kinds of toys.

Now imagine that you want to mix and match the toys, so you take one toy car and one toy train and put them together. This creates a new kind of toy, which we could call a "toy car-train".

But wait, there's more! Imagine you have a bunch of these "toy car-trains" and you want to organize them. You could group them by their color, or their size, or maybe by which toy car and toy train they were made from. This would create different categories or groups of toys.

A double groupoid is kind of like a fancy way of organizing these groups of toys, but instead of just two categories like toy cars and toy trains, there are two different kinds of relationships between the toys. We could call these relationships "horizontal" and "vertical".

The "horizontal" relationship is like putting together a toy car and a toy train to create a "toy car-train". The "vertical" relationship is like organizing the "toy car-trains" into different groups based on which toy car and which toy train they were made from.

So a double groupoid is like a way of organizing things based on two different kinds of relationships. It might sound complicated, but it's actually a really useful tool for mathematicians and scientists to study how different things are related to each other in more than one way!