  The identification of topological Weyl semimetals has recently gained
considerable attention. Here, we report the results of density-functional
theory calculations regarding the magnetic properties, the electronic
structure, and the intrinsic anomalous Hall conductivity of the title compound,
which was synthesized already 50 years ago but received little attention,
hitherto. We found Cs$_{2}$Co$_{3}$S$_4$ to be a ferrimagnetic half-metal with
a total spin magnetic moment of about 3 $\mu_B$ per formula unit. It shows
energy band gap of 0.36 eV in the majority-spin channel and a pseudo-gap at the
Fermi level in the minority-spin channel. We identified several sets of
low-energy Weyl points and traced their dependence on the direction of
magnetization. The intrinsic anomalous Hall conductivity is predicted to reach
a magnitude up to 500 $\Omega^{-1}$cm$^{-1}$, which is comparable to values
obtained in other celebrated Weyl semimetals.
