Resembling, containing, or characteristic of caves; having cave-like qualities.
From 'cave' (Old French 'cave' from Latin 'cavus') plus '-y' (adjectival suffix); means 'having the qualities of caves.'
The '-y' suffix in English is wonderfully economical—adding it to almost any noun creates an adjective, which is why 'cavey,' 'rocky,' 'sandy' all feel instantly natural.
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