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Results tagged with homological-algebra
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user 3969
(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
0
answers
108
views
When is a chain complex induced up to quasiisomorphism
I have a field extension $F/F'$ and an algebra $L'$ over $F'$. Let $L$ be the induced $F$-algebra $F\otimes_{F'}L'$ and $C_*$ a chain complex over $L$.
Is there a good way to decide whether $C_*$ is …
- 11.1k
7
votes
Accepted
Question about spectral sequences associated to filtered complexes with unbounded filtrations
Suppose we have $\bigoplus_\mathbb{N}\mathbb{Z}$ and $\prod_\mathbb{N}\mathbb{Z}$. Both modules hava a canonical decreasing filtration where the $k$-th filtration step consists of all elements whose f …
- 11.1k
3
votes
2
answers
170
views
Equivariant maps of "higher order"
Given a group $G$, a ring $R$ and two $R[G]$-modules $M,N$. Then one can consider $Hom_R(M,N)$ and define inductively submodules $A_0,A_1,...$ via
$A_0:=0$
$A_{n+1}:=\{ \;f\; |\; \forall\; g\in G: …
- 11.1k
4
votes
Functoriality of filtered spectral sequences
Let us use increasing filtrations $F^pC \subset F^{p+1}C\subset \ldots$. Then the homology of $C$ and $C'$ also inherit the structure of filtered modules by $F^pH(C) = im(H(F^p(C)\rightarrow C))$, or …
- 11.1k