I work in an Abelian class. If I take the Baer sum of two extensions $M’$ and $M”$ of $
M_2$ by $M_1$, i.e.,
$$ Zero to M_1 to M’ to M_2 to 0$$
is precise, and the identical for $M”$, then what do I learn about $mathrm{Finish}(M’ + M”)$? Do I’ve any entry to it? I do know every little thing I would like concerning the different objects (I do know $mathrm{Finish}(M’)$, $mathrm{Finish}(M”)$, $mathrm{Finish}(M_1)$ and $mathrm{Finish}(M_2)$, and in addition all of their $mathrm{Hom}$ units, for example). I take advantage of the definition of Baer sum as successive pullback and pushout of $M’ oplus M”$ by the diagonal and codiagonal maps on $M_2$ and $M_1$, so a extra common (and possibly simpler) query is: what do I do know concerning the endomorphism ring of the pullback / pushout of two objects, if I do know the objects?
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