  We investigate the impact of different properties of the nuclear equation of
state in core-collapse supernovae, with a focus on the proto-neutron-star
contraction and its impact on the shock evolution. To this end, we introduce a
range of equations of state that vary the nucleon effective mass,
incompressibility, symmetry energy, and nuclear saturation point. This allows
us to point to the different effects in changing these properties from the
Lattimer and Swesty to the Shen et al. equations of state, the two most
commonly used equations of state in simulations. In particular, we trace the
contraction behavior to the effective mass, which determines the thermal
nucleonic contributions to the equation of state. Larger effective masses lead
to lower pressures at nuclear densities and a lower thermal index. This results
in a more rapid contraction of the proto-neutron star and consequently higher
neutrino energies, which aids the shock evolution to a faster explosion.
