Natural transformation

Okay kiddo, let's talk about natural transformations. Imagine you have a bunch of boxes with toys inside them. Each box is like a category, filled with toys that fit into that particular category. Now, let's say you have a grown-up who likes to organize these boxes and move toys from one box to another.

A natural transformation is like that grown-up, but instead of boxes and toys, they are moving things called functors between different categories. A functor is a kind of machine that takes things from one category and turns them into things that belong in another category.

So, a natural transformation is when the grown-up (or the natural transformation) takes one functor and moves it to a different box (or category). And here's the really cool part: the natural transformation can do this for lots of different functors and categories, all at the same time! It's like the grown-up can organize all the boxes in the room just by moving the toys around and making sure everything is in the right place.

And just like the grown-up can move toys from one category to another in a way that makes sense, the natural transformation can also move functors from one category to another in a way that makes sense. This is why it's called "natural" - it's like the grown-up is just doing what feels right and makes sense, instead of forcing things to fit.

So that's what a natural transformation is - it's like a grown-up that moves functors between categories in a way that makes sense, just like how you might move toys between boxes!