short exact sequence of groups

Let \(\mathcal{A}\) be an abelian category and \(G,H,K \in \mathrm{Ob}(\mathcal{A})\) A short exact sequence is an exact sequence of the form

\begin{align*} ... 0 \rightarrow 0 \rightarrow H \underrightarrow{\varphi} G \underrightarrow{\psi} K \rightarrow 0 \rightarrow 0 ... \end{align*}