Fibered category

Okay kiddo, imagine there are a bunch of boxes with toys inside them. These boxes are grouped together based on what type of toy is inside, like all the superhero toys are in one box and all the animal toys are in another box. Imagine each box is a category.

Now, let's say we want to connect the boxes together based on how they're related to each other. For example, we might connect the superhero toys box to the box of comic books because they're related to each other. When we do this, we create a special type of category called a fibered category.

A fibered category is like a bunch of connected boxes, where each box is a category and they're connected based on how they're related. These connections are called fibers, and they're like the strings that tie the boxes together.

When we talk about fibered categories, we often use a special word called a functor. A functor is like a helper that takes us from one box to another. It tells us how the toys or objects in one box relate to the toys or objects in another box.

So, in summary, a fibered category is like a bunch of boxes with toys inside, where the boxes are connected to each other based on how they're related. And functors are like helpers that guide us from one box to another.