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Sounds suspiciously close to The Carpet People, but frankly it's been a while since I've read it.
I give up for now and try later, but I'd like to know:
- if the work is illustrated?
- this chapter, how much of the entire work does it represent?
- is the work a collection or anthology?
- what was the language and/or territory you've seen the work in?
- is it at all possible that the people were normal sized and only the cats were large?
edit:added the second paragraph
Edited by skewview AFK with issues, will return~jormis, I've tried looking for this on isfdb since my previous posting, several times, good reads too, not much luck I'm afraid.
I'm curious if this book was didactic or a sort of creative writing educational aid of some sort. Have you bought it or was it on loan from a library of some sort perhaps? (could be useful in tracking it down in library search).
AFK with issues, will return

Children's chapter book that was read in 90s but possibly older