Cat door in the floor?

I have seen this sort of installation in the movies, but googling doesn't help.
Anybody know where I can find a cat door that is designed to go in a horizontal plane,?? I may as well fit it to the existing hole in the floor I need to repair.
Otherwise any suggestions on how to let a cat in & out though the floor without creating a permanent draft. I had thought about and CC suggested a box with the cat flap in the vertical where the barge boards are normally.
This cat door is to lead into the outside cat run along part of the Western exposure on the side of the house


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