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Results tagged with homological-algebra
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user 142444
(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.
6
votes
0
answers
220
views
Relation between extensions and filtrations
We work in an Abelian category. Consider Yoneda extensions, i.e., the Abelian groups Ext$^n(C,A)$ consisting (for $n \ge 1$) of equivalence classes of exact sequences starting at $A$ and ending at $C$ …
- 533
9
votes
1
answer
350
views
Freyd-Mitchell for $k$-linear categories
I don't know much about the proof of the Freyd–Mitchell embedding theorem and I could not find an answer to my question looking naïvely online, but at the same time I feel like this is the kind of que …
- 533
3
votes
0
answers
208
views
Baer sum and endomorphisms
I work in an Abelian category. If I take the Baer sum $M' + M''$ of two extensions $M'$ and $M''$ of $
M_2$ by $M_1$, i.e.,
$$ 0 \to M_1 \to M' \to M_2 \to 0$$
is exact, and the same for $M''$, then w …
- 533