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Results tagged with abelian-categories
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user 142444
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
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
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