It's funny how much mathematical understanding comes from just sitting with ideas for a few years.

A younger grad student asked me recently why he should care about derived categories, how he should think about them, and if I have any good resources for learning about them...

And like, I 𝑟𝑒𝑚𝑒𝑚𝑏𝑒𝑟 being there a few years ago. I remember looking for reasons to care, and wondering how to work with them and think about them, and I remember wanting good references for learning about them. And what's funny is that I was actually anticipated this! I have a LOT of really detailed notes from that time of my life because I wanted to have resources on hand for the day someone inevitably asked me this.

But looking back at them? I really don't think any of them did it for me! I think I just read dozens of papers that use derived categories freely and eventually stopped being scared. I really think the best advice is to read whatever looks interesting over many years, but it sucks because I know I would have hated that advice, haha.

Anyways, I'm sure older mathematicians will read this and think I'm young for only now having this experience, haha. But that's fine! I love smiling wistfully at younger mathematicians, and hopefully some of you older folks get the same feeling from posts like this ^_^