My choice of title might give the answer away a bit. If you were not sure how to spell coworking when telling people about it then you should check out this site.
doescoworkinghaveahyphen.com (thanks to Alex from IndyHall for making this)
This post was a little more humorous than serious, but I think it will help if we all use the same spelling convention. There is also a great discussion of the reason why the community as a whole has chosen to no hypenate coworking on the Office Nomads website.
Have a great day and good luck with your work.
