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The BaCo_1-xNi_xS₂ system forms a solid solution with an almost Mott like insulating phase when x=0 to a weakly correlated conductor in the Ni end member. This weakly correlated material has a series of interesting topological properties such as a hidden spin polarization due to a Rashba coupling and three dimensional Dirac-like cones close to the Fermi level. Here, I will discuss the temperature dependence of the optical conductivity (σ) of this material. The room temperature real part of σ shows a Drude like peak followed by a linear-in-frequency region. Upon cooling the material there is a spectral weight transfer from about 0.1 eV to 0.3 eV. Interestingly the linear region remains unchanged as a function of temperature. Combining the optical measurements with first principle calculations shows that this spectral weight transfer is a competition between regular carriers and Dirac-like bands.