Contact adhesive, as people have said... But it depends on the carpet/fabric. Some carpet that doesn't have a backing will absorb a bit of glue and the spray on stuff isn't thick enough not to be absorbed, so the paint of stuff from a tin works much better. If the carpet has a backing, then spray on will probably work.

I use Kwik Grip or the alternative Gel Grip or something, it doesn't run on vertical surfaces.

Kwik grip or gel all the way.

Much better than spray on contact adjesives and work with all carpets, backed or unbacked.