3 ms·

Not true: http://www.math.cornell.edu/~oconnor/sia.pdf http://www.math.cornell.edu/~oconnor/sia.pdf https://ncatlab.org/nlab/show/synthetic+differential+geometr

• dsacco 9y ago
  You cannot build all of analysis from category theory. Categories, morphisms and functors are not nuanced enough to encapsulate everything in analysis. The question was not, “Can you restate some results in category theory”, the question was “what cannot category theory build?” What you’re linking to is part of a relatively small corpus outside of e.g. algebraic geometry and topology that has successfully been used for nontrivial results. And as another commenter said, while it can be used for e.g. computation, it is extremely poor for complexity theory. There is a reason why basically any analyst (as opposed to algebraic geometer) will use set theory instead of categories for their work.