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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 …
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 …
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 $C$ …