lgdw

Having a hard time following the lower bound proof, especially this part:

> By the definition of 𝑃𝑎 , we know there are at least as many programs in 𝑃𝑎 as there are artefacts in 𝜋 (𝐺), i.e. |𝑝𝑎 | ≥ #𝜋 (𝐺).

I'm not sure how the definition of P_a leads to |p_a| >= #\pi(G)...

fifth one down.

I remember this being in a NACLO problem last year.

I'm not very familiar with physics, but if I recall correctly the electromagnetic force can be thought of as a Hopf fibration.

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.

Sorry, force of habit.

Yes, this textbook is a great introduction to point-set topology. I'm not very familiar with algebraic topology so I can't comment on anything regarding that. I did learn a fair bit of category theory that I didn't know prior, like a formal explanation of deriving the Yoneda Lemma (I read this book before I read CWM). I think it's definitely possible to learn category theory from this book, especially if you already have a strong intuition for Topology.

I forgot to add that Algebra Chapter 0 takes a similar (albeit slightly different) approach of teaching Abstract Algebra in terms of Category Theory. I don't have a link right now but I'm sure you can find it on libgen. (I've only read the first few chapters of Algebra Chapter 0 yet, but from what I've heard the rest of the textbook is as good as the first bit.)

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.

iirc it is just a mirror of libgen.

It's the actual process of translating everything into boxes and arrows that's the core of ACT.

Yes, that's why I recommend starting out with 7 Sketches.