The Renaisance Italians seemed to have a fondness for extended elevated passageways. The Vatican has one, and Florence has the Vasari Corridor. Vasari was commissioned by the Medici to build the structure and in so doing displayed the power conections of the great banking family.
The corridor starts with this bridge between the Palazzo Vechio, Florence's town hall, and the Uffizi, literally the "offices" of the Medici.
Since the door to the Palazzo Vechio is locked, the space is used as its own office nowadays.
The passageway continues through the famous art gallery and comes out on the river side of the Uffizi.
The corridor precedes along arches and across the river over the Ponte Vecchio.
The end is the Palazzo Pitti, a palace the Medici aquired from another Florentine family.
It just shows you that the skybridges in modern cities are not a new idea, and few of those allow you to go from work to home without going outside.