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Results tagged with big-picture
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Questions designed to get an overview of a specific subject or body of results or to understand the relations among similar definitions, techniques or concepts appearing in different sub-fields of mathematics. While such questions by their very nature sometimes cannot be made very narrow and focused, it can be helpful to keep in mind that the design of MathOverflow does not make it a good fit for questions that are too broad.
53
votes
What is a cohomology theory (seriously)?
I have now newly written a detailed “Idea” section at the nLab entry on cohomology, which should give a helpful overview on the observation that and how every flavor of cohomology ever considered is n …
- 19.8k
17
votes
Accepted
What is the relationship between algebraic geometry and quantum mechanics?
I also would say it's non-commutative geometry and in particular the notion of spectral triple that is the geometric formalism directly coming out of quantum mechanics.
A sketchy description from this …
- 19.8k
13
votes
Accepted
At which level is it currently possible to write formal proofs?
One can possibly make some headway by switching from a traditional formulation of a field of mathematics to a "synthetic" formulation, where the objects under study are not explicitly built out of sma …
- 19.8k
11
votes
Abstract Relation between Presehaves and Simplicial Sets
Yes, so:
A simplicial set is indeed precisely a presheaf on the simplex category.
There are various model category structures on categories of presheaves in general and on simplicial sets in particu …
- 19.8k
11
votes
What do whitehead towers have to do with physics?
Hi Dave,
I only just saw this question now. Maybe I can still react anyway.
The anomalies that we are talking about here mean the following: the action functional of a given QFT may turn out to be n …
- 19.8k
8
votes
What precisely Is "Categorification"?
There is now also an expanded nLab entry on this issue: vertical categorification.
Hopefully this will eventually be further expanded to do justice to this important (albeit vague) notion, but it doe …
- 19.8k