Apparently, the expression "library cat" in English often has a completely literal meaning -- кошка, живущая в библиотеке! The problem of mice and rats destroying books (either to get paper for their nests, or to eat the glue) is a very ancient one, so cats were traditionally welcomed to live in libraries.
So they are mice and rats who in fact aspire to books. Cats are used to restrict access to the literature only.