Cute game with a great concept! I got through the first three levels but I unfortunately gave up on the fourth.
Figuring out where each cat should go was fun, but trying to figure out what each cat actually does sours the game experience for me. Every time I thought I knew what a cat's personality was, I was presented with conflicting information. In the first level, white cats seemed like they could go anywhere, but in later levels, they wanted to be left alone...but sometimes placing them next to another cat was fine? There were multiple other examples of that, where it really felt like the game was making up rules as the game progressed.
I get that figuring out what the cats do is meant to be part of the fun, but in practice it was just frustrating. I played several levels and I'm still not clear on the rules.
If the game gave you a description of what each cat does ("can be placed next to horizontal cats, but not diagonal", or something like that), you'd still have the fun puzzle solving element but the player can have confidence in knowing what the rules are. Because if a player isn't clear on what the rules of a game are, they get frustrated. Fix that, and I could see myself playing this for hours.
Also, bonus points for letting us pet the kitty. Pat, pat, pat, pat.