Abelian 2-group

An abelian 2-group is a type of mathematical object that has some special properties. It's like a special kind of toy that you can play with.

To understand what an abelian 2-group is, first you need to know what a group is. A group is a set of objects that you can "combine" in certain ways. For example, if you have 2 apples, you can combine them by putting them both in a bowl. If you have 3 balls, you can combine them by stacking them on top of each other.

But not all combinations are allowed. For example, if you have 2 balls, you can't combine them by putting one inside the other. That just doesn't make sense! Similarly, if you have 2 apples, you can't combine them by taking a bite out of both at the same time.

So a group is a set of objects with a certain set of "rules" for how you can combine them. We call these rules the "group axioms".

Now, an abelian 2-group is a special type of group where:

- All the objects in the group can be represented using only 2 symbols (usually 0 and 1).
- The combination operation is "addition" (like adding numbers).
- Every object in the group has an "inverse", which means if you combine it with another object, you get back to where you started.
- The group is "abelian", which means that the order you combine the objects doesn't matter. For example, if you have object A and object B, combining them in the order "AB" is the same as combining them in the order "BA".

So, an abelian 2-group is a special type of toy that you can play with, where you have a set of objects that you can combine using addition, as long as you follow the group axioms. And because it's abelian, the order you combine them doesn't matter!