system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: What is Category Theory?
gpt
As math progressed through the 20th Century, we kinda realized that there were tons of relationships between various mathematical objects that looked the same but weren't actually related at all. This was a bit because we tend to look at the components that make up a mathematical object, like elements of a set, numbers, points in a space, loops in a space, operations, equations, etc, etc, etc. But, if instead we looked at mathematical objects themselves as the constituents of a theory as a whole, we could illuminate what these theories are a little bit better.

For instance, we have the theory of sets. And when we look at things in terms of set theory, we generally want to know what things make up the elements of a particular set. But the category theory of set theory does not care. It cares about how different sets relate to each other, and the way sets relate to each other is functions between them. So instead of understanding the set A by asking what its elements are, we understand the set A by asking what are all the functions from A to other sets. 

This mindset is incredibly useful, because it allows us to ignore unimportant specifics and focus on the important structural components instead. Moreover, it allows us to explicitly compare different theories together. We can transform the theory of topological spaces into the theory of linear algebra, allowing use to easily conclude tough things about weird spaces using simple algebra. 

**TL;DR:** Look at the relationships between things, rather than the components of a thing.