ELI5: Explain Like I'm 5

Fundamental group scheme

Okay kiddo, let's imagine we have a really cool puzzle. It has lots of pieces that fit together perfectly, kind of like a jigsaw puzzle. But instead of being a regular picture puzzle, this one is a puzzle of how things are connected to each other.

Now, imagine you have a group of friends who all want to help solve this puzzle. Each friend is like a piece of the puzzle – they are unique and fit in a special way.

The fundamental group scheme is like a way to keep track of how all these friends (or puzzle pieces) are connected to each other. It's a special tool that helps us understand the shape and the connections between the different pieces of our puzzle.

Just like we can keep track of which pieces fit together in a jigsaw puzzle, we can use the fundamental group scheme to keep track of how different parts of our puzzle are connected together. This is important because it helps us understand how everything in our puzzle is related to each other and how we can move things around without messing up the whole picture.

So, to recap – a fundamental group scheme is like a really helpful tool for understanding how different parts of a puzzle (or a shape, or anything else really) are connected to each other. It helps us keep track of all the different pieces and how they fit together perfectly.