  In a recent article Facchini and Finocchiaro considered a natural pretorsion
theory in the category of preordered sets inducing a corresponding stable
category. In the present work we propose an alternative construction of the
stable category of the category $\mathsf{PreOrd} (\mathbb C)$ of internal
preorders in any coherent category $\mathbb C$, that enlightens the categorical
nature of this notion. When $\mathbb C$ is a pretopos we prove that the
quotient functor from the category of internal preorders to the associated
stable category preserves finite coproducts. Furthermore, we identify a wide
class of pretoposes, including all $\sigma$-pretoposes and all elementary
toposes, with the property that this functor sends any short $\mathcal Z$-exact
sequences in $\mathsf{PreOrd} (\mathbb C)$ (where $\mathcal Z$ is a suitable
ideal of trivial morphisms) to a short exact sequence in the stable category.
These properties will play a fundamental role in proving the universal property
of the stable category, that will be the subject of a second article on this
topic.
