Neither Edison nor Latimer invented a light bulb. Most likely Warren de la Rue, around 1840, made the first light that was a glowing filament inside an evacuated bulb.
Both Edison and Latimer later advanced the concept towards something commercially viable. It was Latimer whose modifications to a carbon filament made a light that was practical to mass produce and was affordable.
Joseph Swan is who I would see as doing the lion's share of the groundwork, from 1850 - 1878, on developing the filament based bulb.