In the Harry Potter series, the caretaker at Hogwarts School Of Witchcraft And Wizardry is Argus Filch, who has a cat named Mrs. Norris. The cat has the run of the school, and a remarkably close bond with Filch. In fact, she's apparently the only thing he really cares about. That, and puzzlement about her name led Amanda Mannen to pose a fan theory about Mrs. Norris.
To say that Mrs. Norris is an exceptionally smart cat would be like saying Superman is an exceptionally strong dude. Filch and Mrs. Norris often work as a team, patrolling different areas of the castle for misbehaving students. Getting caught by Mrs. Norris is as bad as getting caught by Filch, because she will fetch him straight away. This means that Mrs. Norris has memorized the school's rules, understands them, and recognizes when a student is breaking them. In the first book, Hagrid tells Harry and Ron that he suspects Filch has trained Mrs. Norris to follow him specifically. You'll recognize all of these as things cats can't do. (It's been theorized that Mrs. Norris might be part Kneazle, a cat-like magical creature with superfeline intelligence, but Rowling has shot it down.) She also shows up on the Marauder's Map, while other animals don't. It's almost like she's a person in the body of a cat in a magical universe where that exact thing can definitely happen.
Yes, in this theory, Mrs. Norris is not really a cat at all! Read the various clues that lead to this conclusion, plus speculation on her backstory, at Cracked.