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Results tagged with homological-algebra
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user 25869
(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.
8
votes
2
answers
552
views
Can Ext over a group ring always be expressed as group cohomology ?
Given a group $G$ and $G$-modules $M,N$ with $M$ $\mathbb{Z}$-free then it's well known that
$$Ext_{\mathbb{Z}G}^i(M,N) \cong H^i(G,Hom(M,N))$$
for all $i \ge 0$ (a reference is Brown, Cohomology of …
- 16.2k
34
votes
3
answers
2k
views
Non-split extension of the rationals by the integers
Can someone describe explicitly an abelian group $A$ such that the extension $$0 \to \mathbb{Z} \to A \to \mathbb{Q} \to 0$$ doesn't split ?
Background: The Stein-Serre theorem (Hilton, Stammbach: A …
- 8,501