# Why don’t analysts do category theory?

I’m a mathematics student in abstract algebra and algebraic geometry. Most of my books cover a great deal of category theory and it is an essential tool in understanding these two subjects.

Recently, I started taking some functional analysis courses and I discovered that there is almost no category theory done in these courses. But since most of the spaces studied in functional analysis are objects in categories (e.g. the normed spaces form a category), I find it rather strange that the books leave the category theory out.

Is there a reason for this?

On the other hand, abstract algebra is very fitting for category theory. We focus on “all” groups or “all” modules over a certain ring. Analysis focuses on particular spaces, continuous/differentiable/analytical functions over $\mathbb C$, for example. The situation is similar with set theory, while a very useful tool for formalizing arguments in the better parts of mathematics – it is often neglected and cast aside as a non-issue.