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Martin Sleziak
Martin Sleziak
4:15 AM
2
Q: Is it ever useful to consider a long exact sequence as a chain complex?

John Wiltshire-GordonHere are two common ways of obtaining chain complexes with vanishing homology: Chain complexes that compute the reduced homology of a contractible space Chain complexes that arise as a "long exact sequence in homology" induced by a short exact sequence of chain complexes These two examples seem...

homological-algebra exact-couples
Exact couple
In mathematics, an exact couple, due to William S. Massey (1952), is a general source of spectral sequences. It is common especially in algebraic topology; for example, Serre spectral sequence can be constructed by first constructing an exact couple. For the definition of an exact couple and the construction of a spectral sequence from it (which is immediate), see spectral sequence#Exact couples. For a basic example, see Bockstein spectral sequence. The present article covers additional materials. == Exact couple of a filtered complex == Let R be a ring, which is fixed throughout the discussion...
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Martin Sleziak
Martin Sleziak
6:43 AM
So in short: use gm.general-mathematics for mathematics questions which do not fall into a particular subfield of mathematics, and use soft-question for questions interesting to mathematicians which are not mathematics questions? — Stefan Kohl 18 hours ago
@StefanKohl Roughly yes. soft-question has a tag excerpt (Questions that are about research in math, or about the job of a research mathematician, without being mathematical problems or statements in the strictest sense. Do not use this tag for easy or supposedly easy mathematical questions.) which I find useful and its current use is OK. I guess the role of gm.general-mathematics will remain a bit vague, but I especially want to exclude it as dedicated trash tag. — YCor 18 hours ago
"mathematics questions which do not fall into a particular subfield of mathematics" could make a good tag excerpt. The current tag excerpt "Questions about mathematics which don't fall into the other arXiv categories. If you have a general question about mathematics but it is not research level, it's off-topic but it might be welcomed on Mathematics Stack Exchange" is quite bad, I think. Questions are usually redirected to MathSE because they're not of research level, not because they're about "general mathematics"; they are often focussed. — YCor 18 hours ago
 

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