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Results tagged with big-picture
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user 717
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.
2
votes
What can't be described by categories?
Well, if you don't impose additional conditions, then of course even the category of all sets does not exist. To define such a category you either have to restrict to, say, sets of bounded rank or you …
- 5,243
45
votes
6
answers
6k
views
Universal definition of tangent spaces (for schemes and manifolds)
Both schemes and manifolds are local ringed spaces which are locally isomorphic to spaces in some full subcategory of local ringed spaces (local models). Now, there is the inherent notion of the Zaris …
- 5,243
83
votes
6
answers
16k
views
What is a cohomology theory (seriously)?
This question has bugged me for a long time. Is there a unifying concept behind everything that is called a "cohomology theory"?
I know that there exist generalized cohomology theories, Weil cohomol …
- 5,243
7
votes
Sheaf cohomology and injective resolutions
In my opinion, all answers go a little too far.
In this (non-topological!) setting I think about this as follows: The aim is to analyze the lack of right-exactness of a left-exact functor $\Gamma:C \r …
- 5,243