My interpretation involves two dream theories.
In the Old School dream analysis (not one I embrace or give much credit to) the objects, characters, and actors in dreams all had a very significant significance. They could be symbolistic representatives of worries, anxieties, or even of happiness, calm and peace.
According to more modern theory, the objects and characters and sequences in your dreams in REM state are connected to recently focussed-on realities in your mind; that is, on events and characters in your real life, which you fussed about, or in the least kept re-hashing in your mind the previous day. The dream sequence is a reflection of randomized embedding of the experiences of lasting significance in your long-term memory.
In my own theory, and this is not supported by any research, the dreams still do have to do with thoughts and preoccupations of the recent past in the life of the dreamer, but the randomization is a counter-effective method to stop the obsessing. In other words, one day you are constantly worried about, for instance, your upcoming school report card or your upcoming work performance record that will determine your annual raise. So you obsess, but next time you dream, the icons of your obsessions will be randomized in order to “clear” your mind as if it were a “slate” in order to make room for new obsessive worries.
In fact, REM sleep is a natural and healthy way to make room for new worries, by way of throwing away the old worries.
Because, surprisingly, worrying is a human trait which is a survival advantage. But too much worrying, or focussing on a single set of unchanging worries is not healthy, not conducive to survival… you must come to terms with things that worry you, and you must obsess about different things, in order to stay competitive in the natural world.
Applied to your dream, in particular, the cat may be a symbol of your obsession in the previous days leading up to your cat-dream of events or people in your life in which you were treated as a cat-toy; or in which a power figure, who may have been your wife, you, your boss, or even a real cat, displayed traditional human interpretation of cat-like qualities, such as being cute, but able to turn on you if you displease it /him / her; or being hedonistic, or torturously sadistic, or quietly loving in an unassuming way, or cunning and manipulative, or else, etc. etc.
Your worries in the past few days may have had to do with your struggle with the God question, or with life and death, or with your grandchild’s well-being, or with your wife’s sexual prowess, or of your own (without trying to imply anything negative or factual, as I don’t know you, I’m only feeling my way in the dark.) Any worries that could be symbolized as a weight sitting on your chest, and which you need to get off it. But this is just one of many possible things. Without knowing the events and worrries in your head that you’d been re-hashing over and over in your mind the day or days leading up to the cat-dream, one can’t say what the real meaning of the dream is. And in fact, it is not important… knowing the reason you had that symbol and why you had it has no significance, in terms of future behaviour or omens or learning about the past… if my theory is correct… because the ONLY significance of the symbol appearing in your dream is that it has undergone the randomization, which makes it evaporate as a worry.