More on category theory

While reading this mildly entertaining discussion (among mathematicians) on the merits and misdemeanours of category theory, i’ve stumbled upon this sci.physics.research thread (also available here) with the subject How does category theory help?. The thread starts with a skeptic tone, as exemplified by this fun quote:

is almost impossible for me to read contemporary mathematicians who, instead of saying Petya washed his hands,” write simply: There is a t1 < 0 such that the image of t1 under the natural mapping t1 -> Petya(t1) belongs to the set of dirty hands, and a t2, t1 < t2 <= 0, such that the image of t2 under the above-mentioned mapping belongs to the complement of the set defined in the preceding sentence.”

but of course there’s many a post defending CT, as well as a lot of (i’m actually tempted to say, every single one you’ll ever need) references to papers, books and everything categorical [1]. You’ll find in there all the usual suspects (Baez, Weiss, …) engaged in a very civilized and informative exchange about virtually every single topic related to CT (including lambda calculus and its application to physics!) and then more, like comments on Arnol’d’s geometrical way of thinking (to name a random issue that caught my eye).

As for me, the jury’s still out, although the more time i spend far from (theoretical) computer science, the less i find CT appealing in physics. On the other hand, when i’m just trying to play some maths, CT is really fun in its own sake and i have the nagging suspicion that i like it because it is sometimes posed as the unified theory of math. Whatever.


[1] If you just want a quick link to references to get started, follow this one to a post by Chris Hillman (author of his own Categorical Primer).

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