"A Borgean library" is a reference to Jorge Luis Borges' story "The Library of Babel" (in Labyrinths: selected stories and other writings):
When it was proclaimed that the Library contained all books, the first impression was one of extravagant happiness. All men felt themselves to be the masters of an intact and secret treasure. There was no personal or world problem whose eloquent solution did note exist...[54-55]

There are official searchers, inquisitors. I have seen them in the performance of their function: they always arrive extremely tired from their joureys; they speak of a broken stairway which almost killed them; they talk with the librarian of galleries and stairs; sometimes they pick up the nearest volume and leaf through it, looking for infamous words. Obviously, no one expects to discover anything...[55]

On some shelf in some hexagon (men reasoned) there must exist a bookwhich is the formula and perfect compendium of all the rest: some librarian has gone through it and he is analogous to a god...[56]

I venture to suggest this solution to the ancient problem: The Library is unlimited and cyclical. If an eternal traveler were to cross it in any direction, after centuries he would see that the same volumes were repeated in the same disorder (which, thus repeated, would be an order: the Order). My solitude is gladdened by this elegant hope. [58]

Now aren't you glad you asked?