There are nominalists concerning abstract objects, i. e. they think that only concrete things exist. (Assuming the abstract/concrete distinction is exhaustive) Is it inconsistent with such a nominalism to claim that "abstract object" denotes an "ontological category"? Or, in other words, is there for every ontological category at least an a priori possibility that something exists which is of that category? I'm pretty sure that the expression "ontological category" is sometimes used in a matter which would suggest a YES to these questions and sometimes in a matter which would suggest a NO. But is there something like a standard meaning of "ontological category" regarding these questions?
Ontological categories are categories of being. If 'exists' means 'is in spacetime' or 'exists physically', then abstract objects can still be considered an ontological category, without any patent contradictions with the view that such objects don't have (physical) existence. If, however, 'exists' means 'exists simpliciter', then how can one deny abstract objects any existence and then claim that they belong to a category of being? Under this interpretation, your definition of nominalism is indeed incompatible with the claim that abstract objects constitute an ontological category.