  Topological quantum chemistry (TQC) is a successful framework for identifying
(noninteracting) topological materials. Based on the symmetry eigenvalues of
Bloch eigenstates at maximal momenta, which are attainable from first
principles calculations, a band structure can either be classified as an atomic
limit, in other words adiabatically connected to independent electronic
orbitals on the respective crystal lattice, or it is topological. For
interacting systems, there is no single-particle band structure and hence, the
TQC machinery grinds to a halt. We develop a framework analogous to TQC, but
employing $n$-particle Green's function to classify interacting systems.
Fundamentally, we define a class of interacting reference states that
generalize the notion of atomic limits, which we call Mott atomic limits, and
are symmetry protected topological states. Our formalism allows to fully
classify these reference states (with $n=2$), which can themselves represent
symmetry protected topological states. We present a comprehensive
classification of such states in one-dimension and provide numerical results on
model systems. With this, we establish Mott atomic limit states as a
generalization of the atomic limits to interacting systems.
