Then says that category theory "does not itself solve hard problems in topology or algebra. It clears away tangled multitudes of individually trivial problems. It puts the hard problems in clear relief and makes their solution possible.".
And doesn't give any examples.
Still sounds useless to me.
The most interesting "application" of category theory that I've seen (as it relates to software engineering) is the connection between databases and category theory, e.g at https://johncarlosbaez.wordpress.com/2018/06/06/applied-cate.... In short, relational schemas are categories, and common data migration operations can very naturally can be described in the language of category theory (functors, pullbacks etc).
So is this application productive? It's nice to be able to describe something that already exists in terms of category theory, and even nicer if those descriptions are concise and satisfying. But does that description enable anything new? Did we get any new migration operations, normal forms, etc?
http://www.categoricaldata.net/help/instancesigma.html
Is there somewhere i can go for a worked example of using sigma?
I wouldn't say that you can't do this stuff without category theory, but it does make it easier / clearer. (Similarly, you can do a lot of geometry without coordinates, but coordinates definitely make some stuff easier / clearer.)
[1] https://www.wikiwand.com/en/Brouwer_fixed-point_theorem#/A_p... [2] https://www.wikiwand.com/en/Eilenberg%E2%80%93MacLane_space
The point, I think, is not that those fields of mathematics have obvious concrete applications to computers, but that they support each other in how they are applied to computer problems. Like, one reason numerical analysis is useful is that it helps you better solve differential equations, a common way to model a linear system. So linear algebra, of course, has these great applications in computers, but they're still pretty indirect because it's not like we program computers by feeding them linear maps (or whatever).