On the cohomology sequence in a semiabelian category

In a semiabelian category, a strictly exact sequence $0\to A\to B\to C\to 0$ of cochain complexes gives rise to the cohomology sequence $\dots\to H^n(A)\to H^n(B)\to H^n(C)\to H^{n+1}(A)\to\dots$. We study conditions for exactness of the homology sequence at a given term.