Giving cats outdoors privileges can be extremely controversial, as you probably know. I have seen some heated discussions online. Without going into that, it may be good to point out that depending on the surroundings and the cat, one may want to weigh the pros and cons of that choice. Good news is, there are ways to give a cat safe and controlled outdoors access, which include harness training/leash walks and adding a catio. These will expose the cat to the sounds and smells of the outdoors, without any of the drawbacks. My cats are pretty keen on hanging out on a tiny fenced in back porch, spending their days in a big playcage that is attached to a window, and being out on a leash. I firmly believe that being used to the sounds and smells of the neighborhood through controlled outdoors access, they are much safer in case they slip out, as well. Even when my indoors feral, who will not let me get near him, managed to weasel out, he stood at the door an hour later and wanted to come back home.
There are also various resources and advice from behaviorists. Jackson Galaxy has covered how to train cats to stay away from the front entrance in his show. His book Total Cat Mojo is excellent, and the two books on Catification have an abundance of ideas on environmental enrichment. Pam Johnson-Bennett has great information about training cats to stay away from the door in Think Like a Cat. The Indoors Pet Project at Ohio State has a lot on cats' territorial needs and how to meet these needs by providing environmental enrichment in a home.
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