[l__l]

This is my field :)

Category theory is about connecting the dots between different areas of maths. The "general application" is to allow you to reason over the structure of a problem you're interested in, while throwing away all the superfluous details. It arose when geometers and topologists realised they were working on the same problems, dressed up in different ways. I think the utility for technical people, from this perspective, is pretty clear.

As for the general working person? I think it's just an exercise in learning to do abstractions correctly, which is valuable in any line of work.

There are actually people who advocate that we should base maths education on category theory much earlier (much as New Math was interested in teaching set theory early on, as a foundational topic). CT is an unreasonably effective tool in a large section of pure maths, so this doesn't sound unreasonable to me; it wouldn't be nearly so scary if it were introduced gently much earlier on (in the same way we start to learn about things like induction in the UK in secondary school, long before formalities like ordinals are introduced at uni). Currently only a very specific, highly-specialised section of the population learn CT, but if something like this were to happen, I'm sure we'd see lots of benefits which are hard to identify at the moment.

[throwbadubadu]

Don't need to convince me ;), but I mean this is for the very average person who argues like "why do I need more math than adding two numbers"... and even just "allow you to reason over the structure of a problem you're interested in, while throwing away all the superfluous details" and "learning to do abstractions correctly" would not seem more approachable to them than the calculus description I gave above? imo. Is there a simple real-life problem or model everyone should know or has touched in school this can relate to? I'd be curious, because as you frame it I may even need to revisit my faded memory, hm.

[l__l]

I honestly don't know. This might be a skill issue on my part (very much not an educator), but I think of it as a language for thinking about structural abstraction, so to me the question is akin to "is there a real-life problem that German relates to?"; I can certainly think of lots of problems that would be made much much easier by understanding the language (e.g., getting around Germany, i.e. noticing abstractions), but it's tough to point to anything for this explicit question other than "conversing with someone in German".

I guess to try and mirror your calculus example, I'd try and motivate why someone should care about abstraction itself, perhaps with examples like 'calculating my taxes each year is exactly the same problem, except the raw numbers have changed'.

Alternatively it might go over better to say something like: "Imagine you have a map with a bunch of points, and paths which you can walk between them. CT is the study of the paths themselves, the impact of walking down them in various routes: for mathematicians, this means looking at things like turning sentences such as 'think of a number, add 4 to it then divide by 2 then add 6 then subtract 1' into 'think of a number and add 7'. Once you've spotted this shortcut on this silly toy map, you'll recognise the same paths and the same shortcut when you see on your tax form 'take your income, add £400 to it, divide by 2, add £600 and subtract £100"

[georgeyw]

This text comes to mind: https://math.mit.edu/~dspivak/CT4S.pdf

I've only read pieces of it, but I think this moves in the right direction towards making category theory useful to day-to-day life in non-trivial ways.