From this question and this Wikipedia page, I have now understood the definitions of the Baer sum and of the zero element in Ext$^n(B,A)$. But I still have a couple of questions that I could not find an answer to.
- I still do not understand how to define the additive inverse of a sequence for $n \ge 2$. I have tried to generalize the definition used for $n=1$, but without success. Any hints?
- The definition of equivalence of sequences on the Wikipedia page (which is basically just the existence of a chain map which is the identity on the two extremes) seems very weak, if compared to what I have found in the literature (Bourbaki, MacLane). Above all, it is not at all clear to me why this condition should satisfy transitivity.
To get an additive inverse of $0\to A\to C_1\to\cdots\to C_n\to B\to 0$ in $\text{Ext}^n(B,A)$ just replace one of the maps $A\to C_1$, $C_1\to C_2,\ldots,C_n\to B$ by its negative.