Some do, most don't.

You see the cat looking straight at the camera, grey and white, center frame? She used to smack all the other cats about, especially after we neutered her. She still sometimes leaps at them or swats them, but it's gotten better and she calms down after an instant.

Some of the uncastrated males do fight, but we try to castrate the regulars. But yeah, not a lot of fighting going on, thankfully.