In the Nominative Pronoun lesson, it says that correct translations of this are: each cat, all cats, and every cat. Wouldn't "all cats" be jede Katzen?
The main meaning of 'jede' is 'each one'. If you say 'jede Katze', the image you have in mind is that you have the entirety of all cats in front of you and address each one in turn. Therefore you almost always (there are very few exceptions and they're very special) use the singular with 'jede'. You could also say 'Alle Katzen' for 'all cats'. http://www.duden.de/rechtschreibung/jeder