Yes, go to the bvet site. They will list out exactly all the documents/ vaccinations that are required from your country of export. You can also call them and speak to them in English - I found them very helpful when I brought my 2 dogs and 1 cat from Singapore.

When you book your flight, make sure you ask for a space for your pet. They will ask for the animal's cage dimension.

Upon arrival, I went to the red channel customs, showed them the documents, my proof of residency in CH, let them scan the animals for the microchips and paid my CHF88 and exited all in 10 mins.

As your parents are bringing your cat for you on your behalf, you might want to ask bvet if this is an issue.