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Category theory more than just a language for classifying and organizing existing results. It is the mathematical theory of universal properties (http://en.wiki
by more_original 15y ago
Category theory more than just a language for classifying and organizing existing results. It is the mathematical theory of universal properties (http://en.wikipedia.org/wiki/Universal_property http://en.wikipedia.org/wiki/Universal_property).
In category theory one studies what structure can be captured by universal properties. That is one tries to characterizes structure uniquely by its properties, rather than giving a concrete construction, as is common in set theory. The emphasis on universal properties leads to a different way of thinking and mathematical taste. The study of what one can do in general with universal constructions is thus interesing in itself, though perhaps not for dummies.
Anyway, what I want to say is that while category theory has been overhyped in the context of Haskell, for example, it is not true that it is "completely useless and uninteresting by itself".
- xyzzyz 15y agoThis exactly what I mean by: 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 I just tried to avoid the notions which average HNer is unlikely to know, and understanding them takes too much time. Anyway, I have yet to see a deep and nontrivial result in a pure category theory, and mind you, I have the Mac Lane's book in front of me. Most of it is easy symbol juggling which only result in something interesting when you think what it means in context of concrete structures.