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Results tagged with homological-algebra
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user 178096
(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.
2
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1
answer
417
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Group homology and singular homology
It is well-known that the singular homology of the classifying space of a group $G$ is isomorphic to the group homology of $G$ with coefficients in the trivial $G$-module $\mathbb{Z}$, i.e. $H_*(BG,\m …
- 31
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vote
Accepted
Group homology and singular homology
Indeed, the answer is given in Eilenberg-MacLane's 1945 paper "Relations between homology and homotopy groups of spaces", as pointed out by Chris Gerig.
- 31