Timeline for Moral reason for negative sign in rotation axiom for triangulated categories
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| May 31, 2023 at 8:10 | comment | added | Maxime Ramzi | I think it's not about the zero object, but about the orientation of the square ! implicit in saying "a square X -> 0,0 -> Y gives a map X -> Omega Y" is the choice of an actual square, and thus of an orientation thereof. If you flip the square, you have to account for this in the morphism X -> Omega Y. Another way of phrasing it: Omega Y is the pullback of 0 -> Y <- 0. If you flip the defining pullback square, this gives you a certain map Omega Y -> Omega Y : this is not the identity (think in terms of spaces), it's the map that flips loops, i.e. -1 | |
| May 30, 2023 at 19:14 | vote | accept | JackYo | ||
| May 30, 2023 at 18:59 | comment | added | JackYo | I'm confused a bit. lemma 1.1.2.13 in Lurie's HA follows from 2.10. so essentially if we regard in context of this philosophy the triangulated categories as shadows of stable infty cats, then the sign comes from flipping of explicit choices of two zero objects, right? That looks strange at first glance since as far as I know a zero object is unique. Or does here exactly matter that the uniqueness of zero objects is only given up to iso, so the sign "detects" these as different considered as "bare" objects, even though isomorphic objects? (or do I missing the issue?) | |
| May 11, 2023 at 8:44 | history | answered | Maxime Ramzi | CC BY-SA 4.0 |