Well, if you’ve already got the algebraic background needed for arithmetic geometry then you could probably break into the basics fairly painlessly. I found that my familiarity with algebraic structures from the algebraic geometry side of things has made my readings much smoother than they were the first time I tried to tackle it (near the end of my sophomore year I think?), which was very slow going (I was using Maclane’s CWM and simply didn’t have the appropriate background) and I did not get much out of it. Even if you’re already doing your dissertation or something, it hardly seems like too much of a stretch to switch over.
I’m much earlier than that (only my first year in grad school), it definitely wouldn’t be a problem in terms of my mathematical development to switch to category theory, but there are no real pure category theorists at my school and I’ve just committed to working with a somewhat famous number theorist who has promised to contribute significant money to me gallivanting about Europe this summer at conferences.
Well, if you’ve already got the algebraic background needed for arithmetic geometry then you could probably break into the basics fairly painlessly. I found that my familiarity with algebraic structures from the algebraic geometry side of things has made my readings much smoother than they were the first time I tried to tackle it (near the end of my sophomore year I think?), which was very slow going (I was using Maclane’s CWM and simply didn’t have the appropriate background) and I did not get much out of it. Even if you’re already doing your dissertation or something, it hardly seems like too much of a stretch to switch over.
I’m much earlier than that (only my first year in grad school), it definitely wouldn’t be a problem in terms of my mathematical development to switch to category theory, but there are no real pure category theorists at my school and I’ve just committed to working with a somewhat famous number theorist who has promised to contribute significant money to me gallivanting about Europe this summer at conferences.