The friction-based physics is not commonly used in platformers for the reason of not being very friendly to new players, but I still wanted to give it a go (to learn why it is not used the hard way, lol).
I am not sure why would you want to "stop" the momentum, though. From some players I've heard that the cat barely moves at all, and from your comment it seems like you have an opposite experience. Doesn't your cat stop if you leave it standing on the ground for a second?