- It poured with rain while we tried to put our tent up.
Now, in this sentence the verb to put up means to open something that is folded or rolled up, like the tent in this case, so that it gets ready to be used.
My question is: can I put up a chair, too?
To fold a chair means that we can close that chair, but to open it, could I say: Can I open/put up that chair?
Put up suggests more assembly than a folding chair requires to me.
I would "unfold" a folding chair.