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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.
12
votes
Accepted
Grothendieck - sheaves as meter sticks
Here are two (related) interpretation of this quote I can think of:
A first interpretation is just that Grothendieck was attach to the idea that you can study a 'space' (whatever this mean) by studin …
- 42.4k
36
votes
Accepted
Current status of Grothendieck's homotopy hypothesis and Whitehead's algebraic homotopy prog...
The problem is that the question is highly dependent on the definition of $n$-groupoids. The notion of strict $n$-groupoid is very clear and precise but we know very well (and Grothendieck knew that) …
- 42.4k
73
votes
Accepted
Why did Voevodsky consider categories "posets in the next dimension", and groupoids the corr...
First, there is indeed nothing mathematically very deep in this observation, and I agree that the word "breakthrough" might be exaggerated. But on the other hand lots of very deep ideas look trivial o …
- 42.4k
23
votes
Accepted
Locales as geometric objects
First, if you haven't already you should have a look at this introductory paper by P.T. Johnstone The Art of pointless thinking which gives a lot of insight on how locale theory works.
Here are some o …
- 42.4k