Differential graded category

So you know how sometimes when you're doing your math homework, you have to write down the steps you took to get the answer? That's kind of like what a differential graded category is. It's a way of organizing and keeping track of all the steps you took when solving a math problem.

But instead of just a list of steps, a differential graded category is like a set of instructions you can follow to solve lots of different kinds of math problems. You start with some objects, called "objects" in the category, and some ways to move between them, called "morphisms." But these morphisms have some special properties that make them different than just any old way of moving between objects.

These special properties are called "degrees," and they tell you how "hard" or "easy" it is to move between certain objects. So some morphisms might be really easy to apply, while others are pretty difficult.

But the cool thing is that these degrees all fit together, kind of like puzzle pieces, to make a bigger picture of how all the objects relate to each other. And by following these instructions, you can figure out lots of different math problems.

It might sound complicated, but really it's just a way of organizing information and making it easier to understand. And hey, if you ever become a mathematician, you might get to use one of these things yourself!