  We mainly investigate abelian quotients of the categories of short exact
sequences. The natural framework to consider the question is via identifying
quotients of morphism categories as modules categories. These ideas not only
can be used to recover the abelian quotients produced by cluster-tilting
subcategories of both exact categories and triangulated categories, but also
can be used to reach our goal. Let $(\mathcal{C},\mathcal{E})$ be an exact
category. We denote by $\mathcal{E}(\mathcal{C})$ the category of bounded
complexes whose objects are given by short exact sequences in $\mathcal{E}$ and
by $S\mathcal{E}(\mathcal{C})$ the full subcategory formed by split short exact
sequences. In general, $\mathcal{E}(\mathcal{C})$ is just an exact category,
but the quotient $\mathcal{E}(\mathcal{C})/[S\mathcal{E}(\mathcal{C})]$ turns
out to be abelian. In particular, if $(\mathcal{C},\mathcal{E})$ is Frobenius,
we present three equivalent abelian quotients of $\mathcal{E}(\mathcal{C})$ and
point out that the equivalences are actually given by left and right rotations.
The abelian quotient $\mathcal{E}(\mathcal{C})/[S\mathcal{E}(\mathcal{C})]$
admits some nice properties. We explicitly describe the abelian structure,
projective objects, injective objects and simple objects, which provide a new
viewpoint to understanding Hilton-Rees Theorem and Auslander-Reiten theory.
Furthermore, we present some analogous results both for $n$-exact versions and
for triangulated versions.
