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Results tagged with homological-algebra
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user 1048
(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.
7
votes
1
answer
307
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On the ordered set of real numbers, does sheaf+cosheaf imply constant?
I have a technical question about unbounded chain complexes. I couldn't think of a descriptive title for it.
Let $P$ be a chain complex of contravariant functors on $\mathbf{R}$ (the real numbers reg …
- 4,949
7
votes
Accepted
Calculating Mayer-Vietoris efficiently
To be safe, let me assume the cohomologies are taken with coefficients in a field, like $\mathbf{C}$.
Let $I' \subset I$ be the indices for which $U_i$ is nonempty. The incidence algebra of $I'$ is …
- 4,949
7
votes
When are there enough projective sheaves on a space X?
Here is a sufficient condition. If a space has finitely many points, or more generally has the property that the intersection of even an infinite number of open sets is itself open, then it will have …
- 4,949