It seems that category theory is the new hype — almost nobody actually understands what it is about, or, more importantly, what it is for. Let me tell you what it is for — it’s an important technical tool in mathematical research, which gives you new, coherent language, sometimes provides you with an additional insight in the structure of the stuff you are researching and makes it easier to notice and classify similarities between different kind of structures. Unfortunately, it is almost completely useless and uninteresting by itself — because, well, what’s interesting in objects and arrows anyway?

What make category theory interesting are its connections with various field[s] and [in] math and computer science. That’s why introducing “category theory for dummies” makes completely no sense — it’s like following Erlangen program to teach kids about points, lines and circles on a plane. The need and the significance of Erlangen program arise when you learn about many different geometries, notice what they have in common and what they do not, and try to find out what the geometry is all about. Without it, the Erlangen program is all about abstract bullshit, and the situation is completely the same with category theory. But nobody writes or posts Erlangen program for dummies on HN. Why? “General theory of everything” hype, that’s why. Erlangen program is “general theory of geometry”, but geometry seems a bit pale when compared to everything.

If you really want to understand the significance of category theory, then learn set theory, then algebra, then topology, then algebraic topology and algebraic geometry, or take abstract programming languages theory path. If you don’t care about all this stuff, because you’re hyped on the category theory, then you’re missing the point — it’s like you wanted to learn about algebraic topology, but did not care about algebra or topology.

Also anything that has “for dummies” in title should invariably remind you of Norvig’s essay (google Peter Norvig 21 days).

— xyzzyz 171 days ago

— Hacker News

2012.03.14 Wednesday ACHK