@MaliceVidrine That's not unlike me haha. But usually I spend 100 times as much time trying to figure out the answer myself as the amount of time it takes for Noah or Asaf to give an answer on Math SE or MO.
It really is. It's yet another source of my second guessing. Do I just have a stream of ideas that aren't very fruitful, or do I keep giving up on decent ideas too soon? I'm pretty sure one of these is true, but I don't know which.
@MaliceVidrine It's helpful to have a friend to bounce ideas off. Unfortunately, those with aligned interests and background are hard to find too haha..
And my interests keep drawing me to the intersection of New Foundations and topos theory, so basically the tiniest sliver in all of mathematics. I don't usually mind my eccentricity but I may have made a terrible mistake.
I'm an obsessive rat-fancier, 80% of what I watch is horror movies, I write storylines for roleplaying games that draw equal inspiration from Robert W. Chambers and Douglas Adams, and my bookshelves feature Aleister Crowley about as prominently as they do Peter van Inwagen and Neil Gaiman.
Which is to say nothing of the incompetence with which I handle virtually every social interaction.
They're both very comfortable with and very practiced in traditional model theoretic techniques, so the category theory seems alien to them, I think.
And I think they're skeptical (and perhaps rightly so) that there's anything to say with category theoretic tools that isn't just a rephrasing of the usual model theory.
Aleister Crowley as the more recognizable name of the occult literature I have around; Peter van Inwagen as one of the more recent philosophers I've read most of the works of, while also one with eccentric ontological views; and Gaiman as a more recognizable name among the comic books I have around.
I count them as a reasonably representative cross section of the erratic nature of my library and interests.
Anyone who thinks Crowley just seems like a real cool dude has some screws loose. For one, he himself said part of the reasons he moved to America later in his life was to avoid the allegations a young woman made against him... And knowing him, I don't particularly doubt the allegations.
Insofar as I can separate the writings from the person, I like his writings. I don't typically have an opinion about the character of authors I read, unless I think they might have enough of a platform to cause people harm.
@user21820 - Btw, here's the question I was thinking about asking (with the topos-theory, reference-request, soft-question, and intuition tags) math.meta.stackexchange.com/a/4726/102781
Yeah, I just want to delay all the typing as long as possible. It's not a particularly complicated theory, but all of my expository efforts came out really long-winded.
Essentially it's the theory of (a coherent formulation of) extensionality, with a group of set-like permutations $f_{g,n}$ where $g$ is an element of some fixed metatheoretic group, and $n$ is a natural number.
In a language where $\notin$ is a primitive predicate symbol along with $\in$.
For any $n$, $f_{g,n+1}(x)$ is axiomatized so as to be the image of $x$ under $f_{g,n}$. So $f_{g,n}$ is "apply $f_{g,0}$ to everything $n$ steps down into the membership structure"
It's a device needed to make sure the permutations respect the membership structure in the appropriate way, in the context of a language that can't actually express the comprehension instances needed for taking images of functions.
(or at least I think it's needed. I wasn't able to think of a way around it.)