You were also incorrect in stating that the Forbidden City was built by the Yuan dynasty. Although there was an Imperial City (known as "Khanbaliq", meaning "great residence of the Khan" in Turkic languages) built by the Yuan at the same location, the Forbidden City itself was built by the Yongle Emperor, the third emperor of the Ming dynasty. The name "Forbidden City" did not exist until the Ming dynasty either. Since the Ming were ethnically Han, "forbidden" did not mean "forbidden to the Han". According to Wikipedia[0]:

> The Forbidden City, as the residence of the terrestrial emperor, was its earthly counterpart. Jin, or "Forbidden", referred to the fact that no-one could enter or leave the palace without the emperor's permission.

0: https://en.wikipedia.org/wiki/Forbidden_City#Name