Comment on The 5-Second Level

Adele Lopez
Sun, 20 Mar 2022 18:56:49 GMT

Abstracting being a useful move isn't in dispute here. The problem is that it's a path of least resistance, which means that you're liable to choose it without thinking, even when it isn't the best move. Giving yourself the space to notice that choice allows you to make a better choice when there is one.

I've found that even when doing category theory, my lack of this skill has often made things much harder than they needed to be. For example, when I tried understanding the Yoneda lemma as something like "objects are equivalent to the morphisms into them", it never quite clicked, and worse, I didn't even notice that I was missing something important (the difference between the Yoneda lemma vs the Yoneda embedding). A clearer understanding only came when I tried writing an expository proof, and tried understanding the poset version, which were both steps in the concrete direction.

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