Mughal designs and patterns generally came with them from Persian influence. This is apparent in the different types of umbrellas as well as the magnificent Forts Mausoleums and Mosques constructed by the Mughal artisans and architects...In fact the Chhatri which normally means a type of umbrella also appears in stone built form usually on the corners of huge magnificent palaces and fortresses as small domes etc but called the same ..See https://selfstudyhistory.com/2015/0...-during-mughal/
The tendency is to call also the small hand held umbrella a Chhatri...In this case held over one persons head or attached to a throne...The Emperors and in a bigger group may as seen below be seated under the bigger sun shade sometimes called a Saiban (Sunshade) and have single small Parasols raised over them. This tradition is reflected into the marriage ceremony where the bride and groom sit with the Pandit(Holy Man) for their marriage vows.
Babur(Tiger); for a quick resume of his operations see https://www.britannica.com/biography/Babur
for a rapid roller coaster of his incredible achievements as the founder of The Mughal Empire.