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Results tagged with homological-algebra
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user 104682
(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.
18
votes
3
answers
1k
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The isomorphism class of $\mathrm{Ext}^1_\mathbb{Z}(\mathbb{R}/\mathbb{Z},\mathbb{Z})$
In a recent conversation with a colleague, the following question arose:
What is the isomorphism class of $\mathrm{Ext}^1_\mathbb{Z}(\mathbb{R}/\mathbb{Z},\mathbb{Z})$? That is to say, what is …
- 323
4
votes
0
answers
174
views
Quasi-inverse and homotopy invariance of Shapiro's lemma map
I and two of my colleagues are currently wrestling with Shapiro's lemma in the following situation. Let $G$ be a finite group, let $H$ be a subgroup of $G$, let $k$ be an algebraically closed field o …
- 323