A correspondence between entities of different ontological categories can at most be extrinsic and representational, as Kreisel's work on informal rigor suggests proof-theoretic notions must be grounded in their specific domains.
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grounded in(whether distinctness or identity is explained by intrinsic features)
To be explained by or to have its reason or basis in something else—like how a tree being wet is grounded in (explained by) recent rain.
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.
representational(used to discuss whether experiences can be captured in some form that others can understand)
Something that stands for or describes something else—like how words represent ideas, or how a painting represents a scene.