Watched 1.25 videos (basically, where he drops philosophy and ought to get into real explanations), and am starting to feel dissatisfaction I always feel when try to learn about this stuff from programmers. What I always expect is mathematics, explained informally for easier understanding. What I get is not mathematics, I can even say he is starting to sound mystical. For instance, he says "bunch of objects". He understands, that "bunch" is a weird term (actually, not a term at all) and it might seem he could use word "set" instead, but he can't. Why he can't? He doesn't really explain, he just starts delving into some weird narratives of "set-theorists everywhere see set-nails, because they have a set-hammer" and "because paradoxes". But if you actually studied set theory (and I guess every programmer does at some point, or at least should to) you know ZFC was basically created to help to get rid of these paradoxes, so it still isn't clear why a "bunch" isn't a "set".
So you go to the Wikipedia and learn there is a word "class" (no more complex than a word "bunch" at all, in my opinion) and there exists simple, very much set-theoretical explanation of what is (or might be in different set-theory systems) a class, and why it might be not a set sometimes.
Then he starts with arrows, and again, from the explanation it isn't immediately obvious why he can't use a word "function" instead (and it is immediately obvious when you read definition of category on Wikipedia — and I got used to the fact Wikipedia isn't the best source by far when trying to learn math).
So, my real complaint is these guys are consciously not using mathematics (because math texts are "scary" — and, yeah, I agree, they often are) when essentially explaining mathematics. Category theory isn't some different discipline, it isn't "superset" of mathematics — it is mathematics. Informal is good when it isn't "imprecise", otherwise it's just useless and harmful. I sometimes think it might be easier to actually get used to (once more all over again) all math-talk and read something like "Categories for a working mathematician", instead of trying to decipher all these "simpler" informal explanations.
So you go to the Wikipedia and learn there is a word "class" (no more complex than a word "bunch" at all, in my opinion) and there exists simple, very much set-theoretical explanation of what is (or might be in different set-theory systems) a class, and why it might be not a set sometimes.
Then he starts with arrows, and again, from the explanation it isn't immediately obvious why he can't use a word "function" instead (and it is immediately obvious when you read definition of category on Wikipedia — and I got used to the fact Wikipedia isn't the best source by far when trying to learn math).
So, my real complaint is these guys are consciously not using mathematics (because math texts are "scary" — and, yeah, I agree, they often are) when essentially explaining mathematics. Category theory isn't some different discipline, it isn't "superset" of mathematics — it is mathematics. Informal is good when it isn't "imprecise", otherwise it's just useless and harmful. I sometimes think it might be easier to actually get used to (once more all over again) all math-talk and read something like "Categories for a working mathematician", instead of trying to decipher all these "simpler" informal explanations.