2 ms·

So would it be fair to say that category theorists are mostly concerned with categorizing things?

• aleph_minus_one 3y ago
  > So would it be fair to say that category theorists are mostly concerned with categorizing things? The more basic parts of category theory (which even many mathematicians won't be able to surpass) have in my opinion a slight element of this, even though in my opinion there is still more to even this basic level: getting the categorical perspective often gives you elucidations of various areas of mathematics in the sense that it often shows you how some "side definitions" that are studied in some mathematical area (i.e. definitions that are often mentioned in textbooks, but are not central to the study plan of the textbook) turn out to be more important than it seems without having the framework of category theory at hand. But after you have reached this level, you can start formulating deep and far-reaching mathematical conjectures using category theory which would be hard to formulate and appreciate without category theory. Here, category theory goes far beyond categorizing things: new categorical abstractions and conjectures formulated in terms of them often become deep new generalizations of topics studied in long-existing mathematical areas. Just to be clear: this is for mathematics. For computer science, I rather doubt that if the problems that you are working on are not suitable for formulating in terms of category theory, new definitions that would be hard to formulate without category theory are helpful for the computer science topic that you work on. In this sense: in my opinion most currently existing applications of category theory in computer science are indeed about categorizing things.