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Results tagged with homological-algebra
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user 4991
(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.
10
votes
Spectral sequences: opening the black box slowly with an example
Let me elaborate on part of Tyler's answer, and "second" the importance of constructing examples yourself in a setting where that is feasible, namely that of bicomplexes. Even though as you say they …
- 4,990
8
votes
Essential theorems in group (co)homology
Here's one which is key for calculations: Let $H$ be a subgroup of $G$ and $W_G(H) = N_G(H)/H$. Then the restriction map $H^*(BG) \to H^*(BH)$ maps to the invariants $(H^*(BH))^{W_G(H)}$.
When $H$ …