  Compact objects observed via gravitational waves are classified as black
holes or neutron stars primarily based on their inferred mass with respect to
stellar evolution expectations. However, astrophysical expectations for the
lowest mass range, $\lesssim 1.2 \,M_\odot$, are uncertain. If such low-mass
compact objects exist, ground-based gravitational wave detectors may observe
them in binary mergers. Lacking astrophysical expectations for classifying such
observations, we go beyond the mass and explore the role of tidal effects. We
evaluate how combined mass and tidal inference can inform whether each binary
component is a black hole or a neutron star based on consistency with the
supranuclear-density equation of state. Low-mass neutron stars experience a
large tidal deformation; its observational identification (or lack thereof) can
therefore aid in determining the nature of the binary components. Using
simulated data, we find that the presence of a sub-solar mass neutron star
(black hole) can be established with odds $\sim 100:1$ when two neutron stars
(black holes) merge and emit gravitational waves at signal-to-noise ratio $\sim
20$. For the same systems, the absence of a black hole (neutron star) can be
established with odds $\sim 10:1$. For mixed neutron star-black hole binaries,
we can establish that the system contains a neutron star with odds $\gtrsim
5:1$. Establishing the presence of a black hole in mixed neutron star-black
hole binaries is more challenging, except for the case of a $\lesssim
1\,M_{\odot}$ black hole with a $\gtrsim 1\,M_{\odot}$ neutron star companion.
On the other hand, classifying each individual binary component suffers from an
inherent labeling ambiguity.
