How many people who read this story thought of "Alice in Wonderland"? In particular, the Cheshire Cat?
1) The cat is gray with stripes of darker gray, like Teniel's illustration of the Cheshire Cat in Alice in Wonderland.
2) It becomes invisible like that cat.
3) Father Inire's interest in children and telling them stories is like Lewis Carrol.
4) Mirrors leading to an alternate reality was done in "Through the Looking Glass" long before Borges.
5) The doll-like child also seems like a reference to Alice, who shrunk in the story.
6) In the end, the cat haunts someone's dreams. Alice's adventures were dreams.