  We introduce integral structure types as a categorical analogue of virtual
combinatorial species. Integral structure types then categorify power series
with possibly negative coefficients in the same way that combinatorial species
categorify power series with non-negative rational coefficients. The notion of
an operator on combinatorial species naturally extends to integral structure
types, and in light of their `negativity' we define the notion of the
commutator of two operators on integral structure types. We then extend
integral structure types to the setting of stuff types as introduced by Baez
and Dolan, and then conclude by using integral structure types to give a
combinatorial description for Chern classes of projective hypersurfaces.
