What does ‘their’ stand for?

What does ‘their’ stand for?

The passage below is from The Library: A Fragile History by Andrew Pettegree.

Colbert’s shrewd understanding of the power of the library, and the dangers of conspicuous display, was not necessarily passed on to other statesmen. Long after his death, Cardinal Mazarin’s ambitious library programme would inspire many noblemen, diplomats, cardinals and bishops to build their own grand collections, and open them to the public; the librarians they would employ would be humanist scholars like Naudé, instead of astute administrators like Colbert. That the

tribulations of such flamboyance were easily forgotten was largely the result of a persistent culture of emulation. None of the collectors wished to be outshone by their rivals: this competitive spirit was actively encouraged by librarians, who urged the collector to examine carefully what other great collectors owned. Naudé had advised that the collector should copy and improve upon other collections by acquiring copies of their book catalogues. Emulation was made possible because great collectors were eager to show off their libraries to visitors; on diplomatic missions and on the grand tour, famous libraries became an essential destination for cultured envoys, bishops and young noblemen, keen to make their impression upon the world. Contacts made on foreign trips would also play an important role when the collector had returned home; a trusted correspondent who could seek

out and acquire art, curiosities and books for their patron was a vital requirement for any serious collector.

I want to ask what ‘their’ stands for?

It seems like to refer to ‘cultured envoys, bishops and young noblemen’ in a way, but also represent ‘famous libraries’ in another.

Or is it just the author’s failure to be specific?

Thanks in advance.