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Results tagged with big-picture
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user 2625
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.
45
votes
8
answers
14k
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How should one think about sheafification and the difference between a sheaf and a presheaf
The first time I got in touch with the abstract notion of a sheaf on a topological space $X$, I thought of it as something which assigns to an open set $U$ of $X$ something like the ring of continuous …
- 2,782
30
votes
12
answers
14k
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Why are tensors a generalization of scalars, vectors, and matrices?
Take two vector spaces $V$ and $W$ over a field $F$. One may form the tensor product $V\otimes W$ and it fulfills an universal property. Elements of $V\otimes W$ are called tensors and they are linear …
17
votes
2
answers
3k
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Why does homotopy behave well with respect to fibrations and homology with respect to cofibr...
(I apologize that this is a vague question).
I seems to me somehow that homotopy groups behave well with respect to (Serre)-fibrations. For example you get a long exact sequence of homotopy groups fr …
- 2,782
11
votes
1
answer
936
views
Analogue to Serre spectral sequence for cofiber sequences and homotopy
(This is a follow-up question to this one).
As it is nicely outlined in an answer to this question, homotopy groups behave well with respect to (Serre)-fibrations and (co)homology groups behave well …
- 2,782