A tate-eboshi (烏帽子, lit. "standing eboshi cap") is a tall, straight hat worn by Japanese male aristocrats since the Heian Period. Afterwards, various types of eboshi were born, e.g. Kazaori eboshi (Samurai eboshi), Okina eboshi, etc. Tate eboshi is the best-known one. This headdress came about in the Heian period based on headgear known as a hashiha-kouburi (圭冠).
Kanmuri are official hats worn in the imperial court and eboshi are casual headdresses worn by the nobility and it was also worn by the normal people. The Mikado never uses an eboshi. Danbooru currently does not distinguish eboshi from ancient Japanese kanmuri (冠).
Physically, the kanmuri stands out thanks to the "koji (巾子)", a cylindrical shape that stands upright from the top of the headwear, and the "ei (纓)", string-shaped cloth which hangs down from the rear of the headwear towards the wearer's back. The Japanese at the time when kanmuri were still simple sack-like shapes had a topknot on their head. They wore kanmuri by putting the topknot through a tube and binding the root of the topknot wearing this sack and letting the rest of the string hang down their backs. The terms "koji" and "ei", which were used even when the shape and quality of the kanmuri changed, serve as a reminder of this older form.