How to keep a cat indoors with a dog door?

OK so here's the deal..... I have one dog now a 3 year old black lab. She is very good she never runs away from me and is hardly ever on a leash. This summer we are going to get a new lab and maybe a cat later but I mean way later like Christmas or later. I'm trying to convince my dad to get a cat but I don't want it to run away and we have a dog door that's in the wall. Please can you tell me ways to have the cat not running out the dog door. Please don't say that dog door with the collar because its expensive and only comes with 1 collar but we will have 2 dogs. Thanks

I have 1 dog & 1 cat. They are very good. I'm trying to encourage my dad to get a cat but I don't trust for it to run gone and we have a dog door that's in the wall. Please don't say that dog door with the collar because it’s expensive.

Dog doors exist for two reasons. Lazy owners and spoiled dogs.

Hi! Most cats donot run away out of a dog door. The flap is a heavy rubber piece and is difficult for the cat to push open. If you are keeping the cat inside then it will get aquainted to indoor life and will not go outside as inside cats are usually lazy and spoiled. Just don't worry about it! The cat won't use it!But if you are still not convinced use a lemon. Scratch the peel with your nails and rub it all over the dog door flap. Cats HATE the smell of lemons!

cats do not just run away for the sake of it. Their sense of direction and familiarization is extremely good and they never get lost. Cats will venture outside only when they choose. They love to explore but are always cautious and do not want to go far for risk or dangers or crossing other cats territories. They are defensive & protective & will always seek or stay close to the comfort of their own home where they feel most safe & secure & where they are fed. The outside world is for fun, hunting & play only. The security of your house is always where they will come back to without a doubt so do not worry so much. They are clever animals...