Chow group of a stack

Imagine you have a big pile of blocks in the middle of a room. Each block represents an object, like a house or a car. But some blocks are the same as others, just in a different position or with a different color.

Now imagine you want to know how many different types of objects are in your pile of blocks. You could go through and count each individual object, but that could take a long time and might not be very accurate if some objects are very similar.

Instead, you can group the objects that are the same together into a smaller pile. This smaller pile represents all the different versions of that one type of object. You can do this for each type of object in your big pile, and now you have a bunch of smaller piles that represent all the different types of objects.

The Chow group of a stack is kinda like that. A stack is a collection of mathematical objects called schemes. The Chow group is a way of grouping together certain mathematical objects called cycles that are similar to each other. Just like how you grouped together the similar blocks in your big pile.

But instead of just grouping them together for fun, mathematicians use the Chow group to study the properties of the stack. They can use it to help understand how the objects in the stack relate to each other, and how they can be transformed through different mathematical operations. It might sound complicated, but it's just like sorting blocks!