Timeline for Definition of an n-category
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 25, 2021 at 13:55 | comment | added | David White | @Student I recommend you ask that as its own question. Your question last year was well-received and you might get interesting answers to this new question. But this comment thread is the wrong place to get into it, because it's not an easy question. | |
| Nov 25, 2021 at 11:05 | comment | added | Student | Coming back to this thread one year later, I now wonder a more fundamental issue that has been addressed in the introduction of Leinster's 2001 survey: In which possible way can we ever prove that two $n$-categories are "equivalent", before the notion of equivalence is established in a well-defined $(n+1)$-category?? | |
| Nov 1, 2020 at 12:32 | comment | added | David White | @DenisNardin Thanks, that is helpful to know. | |
| Nov 1, 2020 at 12:29 | comment | added | Denis Nardin | @DavidWhite Small nitpick: as far as I know the Ayala-Francis proof of the cobordism hypothesis is still incomplete (if that's not the case, I'd love to see a reference filling the gap!) | |
| Oct 30, 2020 at 12:01 | comment | added | David White | @Student sounds like you might be interested in Carlos Simpson's paper "Some properties of the theory of n-categories" arxiv.org/abs/math/0110273v1 Of course, this is from 2001 so by now maybe more is understood. | |
| Oct 29, 2020 at 19:52 | comment | added | Student | Thanks for the update for the state of the art! Are there examples that are known to be inequivalent, but both are still considered by the "mainstream"? And do people expect there to be a set of axioms for higher cats like Eilenberg-Steenrod for cohomology homology, that will pin down what a higher cat is? | |
| Oct 29, 2020 at 19:47 | vote | accept | Student | ||
| Oct 25, 2020 at 3:34 | comment | added | Alexander Campbell | As a higher category theorist who lives in Sydney, Australia, let me come along and say "$(\infty,n)$-categories are the right thing" (which isn't to say that anything else is the wrong thing). I don't agree with the sharp distinction you draw between higher category theory and homotopy theory; as far as I'm concerned, $(\infty,n)$-categories are a part of higher category theory. I mostly agree with the rest of your answer! | |
| Oct 24, 2020 at 15:25 | history | answered | David White | CC BY-SA 4.0 |