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Results tagged with homological-algebra
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user 142651
(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.
4
votes
1
answer
167
views
When does $FP_n(R)$ imply $F_n$?
It is known that if a group $G$ is of type $F_2$ (finitely presented) and of type $FP_n(\mathbb{Z})$, then $G$ is of type $F_n$.
However, is this true also for other rings which are not $\mathbb{Z}$? …
- 321
5
votes
1
answer
326
views
Extension of $FP_{n}$ group
I am reading a paper (Finitely presented residually free groups by Bridson, Howie, Miller III, and Short, Theorem 5.2) where they write the following:
Since $S_{0}$ is a group of type $FP_{n}(\mathbb …
- 321
7
votes
Accepted
Extension of $FP_{n}$ group
If $0\to A \to B \to C\to 0$ is a short exact sequence of groups and $A$, $C$ are of type $FP_{n}$, then so is $B$. Reference: Proposition 2.2 in Homological finiteness properties of fibre products by …
- 321