The mathematical ontology can contain at least two components (1) the literal ontology which doesn't deal with symbolic elements and (2) the symbolic ontology. I already specified that the core mathematical collection types are sets, multisets, and sequences. So the literal ontology could include things like sets of sets, multisets of sets, sets of multisets, multisets of multisets, sets of sets of sets, and so on well multisets of sequences and sets of sequences are multirelations and relations respectively. Each of these different types of classes form different elements of the mathematical ontology constructed just from core data types.
The symbolic ontology can include symbols like the symbols referring to addition and multiplication, and in this way, it can deal with all the other types of data structures encountered in mathematics. All mathematical structures must be representable by some finite symbolic structure in order for them to be reasoned about. So we can classify types of polynomials like univariate polynomials, quadratic univariate polynomials, linear univariate functions, multivariable polynomials, etc. Lattice polynomials can be formed symbolically as related to lattices from abstract algebra. Eventually, even differential equations can be represented as symbolic expressions.
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