Hi Zetetic! Your curriculum is very interesting, in particular referring to “the link between category theory and cognitive science”. Are you talking about this? Or something else? I’m quite fond of category theory but AFAICR I’ve never stumbled upon such a link… Any pointer is really appreciated.
Here is something I found interesting. The author has a number of papers on this sort of thing. This one is pretty interesting as well. This site in particular led me to a great number of links.
This seemed to be of interest on the more neuroscience-y side of things (though it seems like it is very much along the same lines as the material above). So did this.
I haven’t had time to review all (or even most) of that material, so I don’t know what is good and what is bad. What interests me is that it appears that a lot of researchers like the idea, so it seems reasonable to assume that there is a good chance they are on to something. So, I’ve been spending a portion of my time researching this and studying category theory.
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.
Hi Zetetic! Your curriculum is very interesting, in particular referring to “the link between category theory and cognitive science”. Are you talking about this? Or something else? I’m quite fond of category theory but AFAICR I’ve never stumbled upon such a link… Any pointer is really appreciated.
Here is something I found interesting. The author has a number of papers on this sort of thing. This one is pretty interesting as well. This site in particular led me to a great number of links.
This seemed to be of interest on the more neuroscience-y side of things (though it seems like it is very much along the same lines as the material above). So did this.
I haven’t had time to review all (or even most) of that material, so I don’t know what is good and what is bad. What interests me is that it appears that a lot of researchers like the idea, so it seems reasonable to assume that there is a good chance they are on to something. So, I’ve been spending a portion of my time researching this and studying category theory.
Man that is super interesting.
This almost wants me to switch from arithmetic geometry to category theory...
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.