The equation \( ^{146}\text{C} \to ^{147}\text{N} + 0^{-1}\text{e} \) represents beta-minus decay.
In this process, a carbon-146 nucleus emits a beta particle (an electron, \( 0^{-1}\text{e} \)), which results in the transformation of a neutron into a proton, leading to the formation of nitrogen-147.
Therefore, the correct response is:
beta-minus decay.