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Trapping of atoms and molecules in electrostatic, magnetic and optical traps has enabled studying atomic and molecular interactions on a timescale of many seconds, allowing observations of ultra-cold collisions and reactions. Here we report the first magnetic deceleration and trapping of neutral carbon atoms in a static magnetic trap. When co-trapping the carbon atoms with oxygen molecules in a superconducting trap, the carbon signal decays in a non-exponential manner, consistent with losses resulting from atom-molecule collisions. Our findings pave the way to studying both elastic and inelastic collisions of species that cannot be laser cooled, and specifically may facilitate the observation of reactions at low temperatures, such as C + O2 --> CO + O, which is important in interstellar chemistry.