Anonymous at Wed, 3 Jul 2024 03:54:57 UTC No. 16265379

>>16265372
What is a sheave?

Anonymous at Wed, 3 Jul 2024 04:10:26 UTC No. 16265402

>>16265379
A sheaf roughly gives a way to collate local data together in such a way that gives a coherent global picture.
In topology, if you want to talk about some local property, you talk about that property in some open neighborhood of each point; in other words, you describe something locally by describing it on open sets.
A presheaf (of sets, groups, rings, etc) describes some local data; it is an assignment of a (set, group, ring, etc.) to each open set of the topological space in such a way that you have restriction maps which behave functorially (think nicely).
A sheaf is a presheaf with the additional property that this local data can be glued together nicely to give a global picture.

Anonymous at Wed, 3 Jul 2024 04:14:23 UTC No. 16265404

>>16265372
>Why isn't general relativity framed in the language of sheaves?
It predates sheaf theory, and so it is traditional to simply hold to the terminology of the Ricci Calculus as it was when GR came along.
You might also notice that Special Relativity could be processed efficiently with quaternions, but nobody does that either because they weren't very commonly known back when SR came along.

Anonymous at Wed, 3 Jul 2024 04:14:41 UTC No. 16265405

>>16265372
You’re not going to get good posts about physics in particular on this board.

Anonymous at Wed, 3 Jul 2024 04:29:30 UTC No. 16265423

>>16265372
What the fuck is sheaves anon? Care adding some context before spewing nonsense?

Anonymous at Wed, 3 Jul 2024 04:30:14 UTC No. 16265424

>>16265404
Do you know if anyone has tried reframing GR in terms of sheaves?

Anonymous at Wed, 3 Jul 2024 04:31:15 UTC No. 16265426

>>16265423
Care reading the thread before posting a low-effort reply?

Anonymous at Wed, 3 Jul 2024 04:58:34 UTC No. 16265466

>>16265423
If you don't know what a sheaf is then the question is obviously not for you. Stick to your calculus homework, pajeet. Leave the math talk to real mathematicians.

Anonymous at Wed, 3 Jul 2024 05:02:51 UTC No. 16265470

>>16265466
Oh I’m sorry I don’t know all the linguistical jargon needed to understand your math.

Omg. It’s funny that you think I’m not on your level but don’t understand GR is just a more precise mathematical instrument to mesure time.

Cope and seethe faggot

Anonymous at Wed, 3 Jul 2024 12:59:26 UTC No. 16265889

>>16265470
NTA It's not that you don't know it's that you labelled it as spewing nonsense. You haven't even heard of it before.

Anonymous at Wed, 3 Jul 2024 19:30:58 UTC No. 16266441

>>16265423
read Kashiwara's book on sheaves faggot

Anonymous at Wed, 3 Jul 2024 19:35:44 UTC No. 16266450

>>16265379
Sheaves form the universal model of geometric logic. Geometric logic is intuitionistic and potentially anti-classical.

Anonymous at Wed, 3 Jul 2024 19:40:18 UTC No. 16266459

Sheaves are basically the algebraic analougue of manifolds. GR uses pseudo Riemannian manifolds, no?

Anonymous at Wed, 3 Jul 2024 19:52:33 UTC No. 16266480

>>16266459
the metric is indeed a pseudo-metric but why would that prevent specifying the structure of GR with sheaves? the basic principle is the same, glue the space from spaces with pseudo-metrics and then specify the covering condition to be the obvious one with the space being covered with spaces with pseudo-metrics which agree on the overlaps. this requires defining an equivalence relation on pseudo-metrics but I think this should be doable. two pseudo metrics should be considered equivalent if there is an underlying continuous/smooth transformation of the space which transforms one pseudo-metric into the other one

Anonymous at Wed, 3 Jul 2024 19:55:36 UTC No. 16266486

>>16265372
Because GR is a differential geometry theory and sheaves are an algebraic layer of abstraction. Sure you can formulate GR with sheaves. But that's just intellectual masturbation over unnecessary abstraction while sacrificing the natural intuition that comes with diff geo. Don't be a category theory tranny.

Anonymous at Wed, 3 Jul 2024 20:11:43 UTC No. 16266506

>>16266486
it's not differential geometry, it's pseud-differential geometry

Anonymous at Wed, 3 Jul 2024 20:26:27 UTC No. 16266533

>>16265402
Anon, this is interesting, if you can, pls work on this, it could be an achievement of /sci/ for all the redditards acting like we're wasting our intelligence for not sucking up to their karma economy

Anonymous at Wed, 3 Jul 2024 20:29:49 UTC No. 16266538

>>16266486
Fine, but often new theory comes about when you put an existing theory in a different mathematical picture. Intellectual masturbation is literally how physicists make new theories, you never get anything useful if you merely stick to current models and treat experimental anomalies as "I dunno"

Anonymous at Wed, 3 Jul 2024 20:37:34 UTC No. 16266553

Pretty sure this is similar to what the non commutative geometry faggots are doing