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Results tagged with homological-algebra
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user 95546
(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
votes
Nomenclature question: a morita-invariant way to say finite-dimensional?
If I understand the question correctly, the answer should be "perfect $k$-modules".
1) Take $P = A$ to see that $M$ should be a perfect $k$-module.
2) Perfect $A$-modules are the same as retracts of …
- 111
1
vote
Accepted
How to show the following properties of $Coker(d^{-n-1})$?
Well, how do we conclude that our complex $Z^\bullet$ is quasi-isomorfic to the complex
$$
\cdots \longrightarrow 0 \longrightarrow Coker(d^{-n-1}) \longrightarrow Z^{-n+1} \longrightarrow \cdots \lo …
- 111