Don't understand? I think I co-work... All I need is a laptop and phone to do my job... I have a main office but also work in other offices of my organisation with other people and also work from home sometimes...
Co-working is more typically done my self-employed or those at companies with a very small number of employees. It will be a space owned typically owned by none of those people, but where people sub-contract a bit of space and then use the other shared facilities - connectivity, power, toilets, a kettle etc etc.
The people don't work together in any way, but the sharing of ideas is not uncommon. Co-working might be used by those involved in technology and creative industries, but not exclusively.
My permanent office is in Bristol. At times I work at home, in London, in Melbourne, in Montreal, in Hong Kong and in New York. None of that is co-working.