Programming with Categories
I've read a lot about Category Theory, and I'm amazed at the abstraction level that lets you compose with different mathematical domains (geometry, topology, arithmetic, sets, ...).<p>And yet, the current mathematics relies heavily on the ZFC set theory. Why is that ? (Is that assumption even correct ?)<p>From what I've learned so far, the set theory suffers from Russel's Paradox[0] (does the set of all sets that does not contain itself, contains itself ?). That's what motivated the formalization of Type Theory and the invention of Type Systems in programming languages.<p>According to wikipedia[1], <i></i>some<i></i> type theories can serve as an alternative to set theory <i></i>as a foundation of mathematics<i></i>.<p>It seems to me that the Category Theory fits the description. So why don't we see a huge "adoption" in math fields ?<p>Thank you in advance for your clarifications :)<p>[0] - <a href="https://en.wikipedia.org/wiki/Russell%27s_paradox" rel="nofollow">https://en.wikipedia.org/wiki/Russell%27s_paradox</a>
[1] - <a href="https://en.wikipedia.org/wiki/Type_theory" rel="nofollow">https://en.wikipedia.org/wiki/Type_theory</a>