3 ms·

Here are a few examples. Here's operational transforms from CT [0][1]. Here's probability theory (and thus much of ML) [2][3][4]. Lambda calculus arises as a ce

by tel 12y ago

Here are a few examples. Here's operational transforms from CT [0][1]. Here's probability theory (and thus much of ML) [2][3][4]. Lambda calculus arises as a certain kind of category. Operads form a model for wiring diagrams. Database schemata are categories [5]. [0] http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.46.7744 [1] http://bosker.wordpress.com/2012/05/10/on-editing-text/ [2] ncatlab.org/nlab/show/Giry's+monad [3] arxiv.org/pdf/1410.4432v1.pdf [4] https://golem.ph.utexas.edu/category/2014/10/where_do_probability_measures.html#more [5] http://arxiv.org/abs/1302.6946

gohrt 12y ago
You can cast the broadest abstractions in a categorical light, but that ignores the theoretical details that are 99% of the theory of probability/wiring/databases that is of interest to most scholars and practictioners. Yes, it's interesting, but it's not at all clear that category theory pays back the opportunity cost for someone who is interested in understanding field X beyond the generalized abstraction.
- tel 12y ago
  It's not clear, no. CT is another language for abstraction and the same argument as always hold: languages are equally expressive so it's "just a matter of taste" as to what you use. Category theory emphasizes focusing on the relations between thinfs instead of the things themselves. This can be a natural fit for some theories. For instance, anyone studying probability theory knows that random variables are already functions instead of "objects" but they are the primary thing to study. The CT-minded expression of probability theory is obviously equivalent to the Kolgomorov one, but takes that r.v. emphasis further. You can decide whether or not that's a good thing.