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Results tagged with homological-algebra
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user 41035
(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
1
answer
513
views
Brutal truncation of indecomposable complexes
Let $P^{\bullet} = (P^i, d^i)_{i\leq 0}$ be an indecomposable object in category of complexes bounded above, where each $P_i$ is a finitely generated projective module over an finite dimensional algeb …
- 45
2
votes
1
answer
173
views
Is a inverse limit of indecomposable again indecomposable?
In truth, I do not need in the general case.
Let $R$ be a ring (associative, with unit element) and let $\mathrm{Comp}(R)$ the category of complexes over $\mathrm{Mod}\ R$.
If $\mathbb{N}$ is the na …
- 35.2k