You would upload an image of your cat into a directory and then search through the directory for the cat you wanted to pet. When you clicked on it, a holographic image of the cat would sit in your lap, and you could pet it. The hologram felt just like a cat, but it was transparent. I think that the actual cat could also feel you petting it.
My kitty, Luke, was lying near me purring, which probably caused me to dream this. I've also dreamt a lot about technology recently. Not sure why, except that many of my relationships seem to incorporate it in some respect any more.