It's much the same for cats. As long as you have the paperwork in order, there's no quarantine. (This assumes we are talking about a regular domestic pet cat.)
Where are you bringing the cat from?
Depending on the regulations of the country and the airline, you can take cats and small dogs in the cabin. The size and weight limit depends on the airline, but it's usually around 7-8kg with the carrier, with space for them to turn around. It has to fit under the seat in front of you, but as long as it's soft-sided and will squish a bit, the airlines are usually OK about it being a bit oversized. The airline is more likely to be careful about brachycephalic breeds, like Persians, in terms of making sure they have enough space. I've flown with cats in the cabin a few times, and it was fine. They have to stay in the carrier the whole time, but they pretty much just sleep.
I've also flown with a dog in the hold, and that was fine, too. He found the move pretty stressful, but I think he was better in the hold than the cabin even if he had been small enough. He wouldn't have liked all the noise and people/carts moving around him. The hold isn't cold storage. If they have live animals in there, it will be kept between 15c-20c (59-68f).
If you have them with you, I'd guess you still have to go to the animal quarantine station by baggage claim #8 to get your import permit and pay the fee before going through customs, but I don't know that for sure.