[bwestergard]

"I learned Category Theory well before learning abstract algebra and topology, and the embedding of Topology in Category Theory was seamless and intuitive; I feel as though this book proves that this new CT-centric view of math education has merit."

Could you tell us a bit more about your educational history and motivations for studying these topics in this order?

[lgdw]

While I was in highschool I attended a lecture by David Spivak on a whim and was fascinated by the field ever since. Before really discovering Category Theory, I was more interested in low-level computer architecture and design (although I'm not very knowledgeable by any means) so I didn't really encounter Category Theory through the means that most Computer Science people do (FP, Haskell, etc). Once I learned Category Theory I became more interested in other fields of math.

[realitygrill]

If one was a young or returning adult with interest but little background in mathematics, would you suggest learning category theory first (assuming the adult is interested)? How would you suggest going about doing this as a path?

[lgdw]

Although it would depend on what kind of fields of math you are interested in (algebra, analysis, topology, etc), I think that you can't really _go wrong_ per se by learning Category Theory first, even if many of the examples/uses of category theory won't make sense at first. Of course, learning Category Theory first is definitely unorthodox; at least in college, you usually first learn basic algebra (Abstract Algebra, Linear Algebra) along with analysis (Complex Analysis, Real Analysis) and "advanced calculus" (Differential Equations, Multivariable Calculus). Fields like Category Theory usually come after that and are taught mostly in grad school, but at its core learning Category Theory doesn't require knowing a lot of prerequisites so I think in terms of accessibility it resides alongside fields like Linear Algebra or Group Theory. An advantage of learning Category Theory first is that once you have a decent grasp of it, you'd have the mathematical vocabulary to describe concepts learned in different fields; a homotopy is a 2-morphism in the category of topological spaces, for example.

That being said, if you like algebra the most, learn algebra first. If you enjoy topology, learn topology. There really isn't a "right place" to start with mathematics, and as long as you avoid fields of math that build heavily on other fields of math like K-theory or representation theory, you'll have a decent starting background in math. Most fields of math, not just Category Theory, have analogues to other fields (and Category Theory acts only to really formalize this connection), so you can't really go wrong with starting with something like Linear Algebra or Group Theory.