Presheaf with transfers

Imagine you have a big box of building blocks. Each block has a letter or number on it. Now, you have a bunch of friends who also have building block boxes with different letters and numbers on their blocks.

But, you all want to play together and build something cool. So, you decide to share your blocks and make a bigger box. But, you don't want to mix up your blocks with your friend's blocks. So, you come up with a system where you can keep track of whose blocks are whose.

This system is called a presheaf with transfers. Basically, it's a way to keep track of where the blocks came from and who they belong to, even when they're all mixed up.

In math, we use presheaves with transfers to talk about things like algebraic geometry. We use them to study things called algebraic varieties, which are kind of like big puzzles made of equations.

With a presheaf with transfers, we're able to tell which pieces of the puzzle (the building blocks) belong to which person (the owner of the building block box). And that helps us understand how the puzzle fits together and works as a whole.

So, in summary, a presheaf with transfers is like a system for keeping track of who owns what building blocks, even when they're all mixed up together in one big box. We use this system in math to study big puzzles made of equations called algebraic varieties.