A better word than 'cathouse' for an outside shelter for 1 cat

I find plenty of hits on Amazon and other sites for Cat kennel.

https://www.thepetexpress.co.uk/outdoor-cat-kennels-shelters/

https://www.amazon.co.uk/s?k=Cat+Kennel&ref=nb_sb_noss_2

Cat hut—has a roof, at least. Or close it—cathut? Cathut! Sounds like a hairball...

Or cattyshack—has walls...and balls, maybe snacks.

A cat folly has a fountain...and a chaise, of course.

A cat retreat has towers, plural, and all the amenities, but everybody knows that.

Per suggestion in comments below:

My cat lay comfortably dry inside her catio, watching the rain fall on the patio…

Now that's really cute, no doubt.

I withdraw my earlier suggestion of catloo because I agree it sounds like a litter box, and moreover would not be immediately obvious to the vast majority of readers. So, herewith is:

Cat cabin or Kitty Cabin

This was mentioned in a comment by @KannE under the cat hut answer, above, but they did not develop it into an answer.

According to Merriam Webster a cabin is a small one-story dwelling usually of simple construction.

See also Sponsor a Cat Cabin on Cats Protection, the site for a British organization. A US organization, Alley Cat Allies has a similar construction, called a KatKabin which can be seen on this link.

The enclosures in a catio may have multiple shelves rising to the top of the enclosure, but a catio is not the same as a cat house, being at least partially exposed to the elements. Houses for felines and canines are almost always one story high and of simple construction. If more elaborate than a cabin, they are cat manses or cat mansions. Although I have never seen one, I am sure a cat mansion exists, probably in the LA region.

PS: From personal experience, I can vouch for the fact that people-cabins can have lofts, and so not all cabins are necessarily on one level.