Searched: variations of Constantinople Imperial Library, Library of Constantinople, Location, bibliotheke Constantinople, ancient library Constantinople, ad nauseum. Also checked here, our Medieval History memories.
Where in Constantinople would the Imperial Library have been located? Right now I'm assuming the First or Second Hill (proximity to government district, palace) but am unsure.
Setting the Second: Same
Searched: Considerable reading of secondary sources, including the Wikipedia article on the Fourth Crusade, the Siege of Constantinople 1203/1204, our archives, Jonathan Riley-Smith's Crusades, etc.
The Fourth Crusade takes Constantinople October 1203, whereupon Alexius IV commissioned them to stay through April 1204. But:
Did any of the Crusaders reside in the city? Would they have been able to travel freely within the city while Alexius IV held it, prior to the usurpation of Alexius V and the second siege?