Even 'the mathematical' spans multiple ontological categories without this being problematic: physical dogs instantiate arithmetic truths, mental operations of multiplication exist, and mental states about mathematical objects exist.
To be a concrete example of something, or to have and display a particular property or category.
mental operations(The statement mentions multiplication as a mental operation you perform when calculating)
Thinking processes that happen in your mind, like when you mentally solve a math problem or imagine something.
mental states(Herder's theory of mind)
Conditions consisting in forces that manifest themselves in people's bodily behavior, conceptually tied to corresponding types of bodily behavior but not reducible thereto
ontological categories(Thomasson's system; used to address mutual exclusiveness and exhaustiveness requirements)
Classifications of purported entities distinguished by the relations of dependence they have or lack — specifically dependence on mental states and dependence on spatio-temporally located objects.
There is an obvious rebuttal on behalf of pluralism, namely that “the linguistic” is a complex phenomenon with parts that belong to distinct ontological categories. This shouldn’t surprise, since even “the mathematical” is like this: Two wholly physical dogs plus two other wholly physical dogs yields four dogs; there certainly is the mental operation of multiplying 26 by 84, the mental state of thinking about the square root of 7, and so on. (2014: 5)