Pigeons can be kept inside and make great indoor pets, a large dog crate does work well provided they have free time too.
However I personally strongly advise against keeping pigeons inside because of the amount of feather dust they produce which can be an irritant. (Pigeon fancier’s lung, see parrot lung for similar) At the very least you will definitely want some kind of air purifier near the cage. My pigeons bathe as often as they want, fly every day and enjoy going out in every rain storm, and I still see huge clouds of powdery dust waft off them when they fluff up and the sun hits it at the right angle. I’m not trying to discourage or scare you in any way, it’s just a fact that makes me uncomfortable about keeping them indoors.
Just a pair or two pairs of pigeons could be kept happily outside in a relatively small space. Other than that I know that indoors a large dog crate works well or you could even build a cage indoors if you wanted to.
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