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Results tagged with homological-algebra
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user 461
(Co)chain complexes, abelian Categories, (pre)sheaves, (co)homology in various (possibly highly generalized) settings, spectra, derived functors, resolutions, spectral sequences, homotopy categories. Chain complexes in an abelian category form the heart of homological algebra.
4
votes
1
answer
543
views
Generators of a certain ideal
In view of Mariano Suárez-Alvarez's answer I see how badly phrased my question was, and decided to rewrite it. The drawback is that some comments of Martin Brandenburg are now incomprehensible, but I …
- 4,416
17
votes
Accepted
"Sums-compact" objects = f.g. objects in categories of modules?
It seems to me the references in this Mathematics - Stack Exchange answer contain the requested information.
EDIT 1. Here is an excerpt from Hyman Bass's book Algebraic K-Theory, W. A. Benjamin (196 …
- 4,416
20
votes
1
answer
970
views
Example of an additive functor admitting no right derived functor
I asked the same question a week ago on Mathematics Stackexchange but got no answer.
What would be a simple example of an additive functor $F:\mathcal C\to\mathcal C'$ of abelian categories such that …
- 4,416
2
votes
0
answers
101
views
Existence of a certain derived functor
This is a sequel to this question.
Let $k$ be a field, let $A$ be the $k$-algebra $k[\varepsilon]$ with $\varepsilon^2=0$, and consider the following three abelian categories:
$\bullet\ \text M(A)$ …
- 4,416