  We consider two preorder-enriched categories of ordered PCAs:
$\mathsf{OPCA}$, where the arrows are functional morphisms, and $\mathsf{PCA}$,
where the arrows are applicative morphisms. We show that $\mathsf{OPCA}$ has
small products and finite biproducts, and that $\mathsf{PCA}$ has finite
coproducts, all in a suitable 2-categorical sense. On the other hand,
$\mathsf{PCA}$ lacks all nontrivial binary products. We deduce from this that
the pushout, over $\mathsf{Set}$, of two nontrivial realizability toposes is
never a realizability topos.
