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Results tagged with big-picture
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user 126667
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.
22
votes
Describe a topic in one sentence.
Algebraic geometry: CommRing behaves a lot like Setop.
12
votes
What are examples of good toy models in mathematics?
The best examples I've come up with come from rational homotopy theory--commutative differential graded Q-algebras as a toy model for spaces and chain complexes of Q-vector spaces as a toy model for s …
12
votes
Accepted
Why the search for ever larger primes?
Well the M in GIMPS stands for Mersenne, and it hasn't been proven that there are infinitely many Mersenne primes. But it's widely believed to be true--in fact there is a conjectural estimate of thei …
- 25.2k
26
votes
What's a groupoid? What's a good example of a groupoid?
Another answer is that a groupoid is a space which has no homotopy groups in dimension ≥ 2. (Analogously a set is a space which has no homotopy groups in dimension ≥ 1.) They arise from taking (homo …
10
votes
Accepted
Are rings really more fundamental objects than semi-rings?
Of course the real question is whether abelian groups are really more fundamental objects than commutative monoids. In a sense, the answer is obviously no: the definition of commutative monoid is sim …
10
votes
Sheaf cohomology and injective resolutions
If you're willing to take for granted that (bounded-below) chain complexes and quasi-isomorphisms are good things to study, then left exact functors have the defect that they do not preserve quasi-iso …
- 25.2k