  We perform an extensive study of the influence of nuclear weak interactions
on core-collapse supernovae (CCSNe), paying particular attention to consistency
between nuclear abundances in the equation of state (EOS) and nuclear weak
interactions. We compute properties of uniform matter based on the variational
method. For inhomogeneous nuclear matter, we take a full ensemble of nuclei
into account with various finite-density and thermal effects and directly use
the nuclear abundances to compute nuclear weak interaction rates. To quantify
the impact of a consistent treatment of nuclear abundances on CCSN dynamics, we
carry out spherically symmetric CCSN simulations with full Boltzmann neutrino
transport, systematically changing the treatment of weak interactions, EOSs,
and progenitor models. We find that the inconsistent treatment of nuclear
abundances between the EOS and weak interaction rates weakens the EOS
dependence of both the dynamics and neutrino signals. We also test the validity
of two artificial prescriptions for weak interactions of light nuclei and find
that both prescriptions affect the dynamics. Furthermore, there are differences
in neutrino luminosities by ~10% and in average neutrino energies by 0.25-1 MeV
from those of the fiducial model. We also find that the neutronization burst
neutrino signal depends on the progenitor more strongly than on the EOS,
preventing a detection of this signal from constraining the EOS.
