Infinity Castle

The Infinity Castle, also known as the Dimensional Infinity Fortress, was the primary location of the Infinity Castle Arc. The Blood Demon Art and domain of the Biwa Demon Nakime, it is a vast extra-dimensional space that serves as the lair of Muzan Kibutsuji and the Upper Ranks of the Twelve Kizuki.

History
The Infinity Castle first appears when Muzan calls the Lower Ranks to a meeting in which he decides to dismantle them, killing them all apart from Lower Rank One, Enmu, who he lets live as his sadistic personality and honour to die by his hand was seen as the right mindset by the Demon King.Nakime was responsible for summoning each member to the castle, through her biwa.

Following the deaths of the dual holders of Upper Six, Daki and Gyutaro, Muzan, through Nakime, subsequently summoned all of the remaining Upper Ranks to the Infinity Castle to relay his disappointment in them and to discuss a new plan of action. Kokushibo was the first to arrive to the castle, while Akaza was the last.

After the deaths of Gyokko and Hantengu, as well as the revelation of Nezuko Kamado being immune to the Sun, Muzan gathers all of the demons in the country and turns them into mindless demons with the strength of a Lower Rank. These demons would later be seen as cannon fodder to be used against the various members of the Demon Slayer Corps.

During the final assault against demons by humanity, the castle held many notable battles. These included Doma's clashes with Shinobu, Kanao, and Inosuke, Tanjiro and Giyu battling Akaza, Muichiro, Genya, Gyomei and Sanemi facing Kokushibo, Zenitsu's duel with Kaigaku, and Mitsuri's and Obanai's skirmish with Nakime. Preceding this was the initial confrontation of the Demon Slayers and Muzan, with Tamayo joining the clash in order to poison the Demon King with a special drug. When the Demon Slayers converged on a restrained Muzan, Nakime opens numerous doors beneath them, causing them to fall into the castle.

During the second clash of the Demon Slayers against Muzan, Nakime was controlled by Yushiro in order to prevent him from seeing Mitsuri and Obanai, having used a talisman of his Blood Demon Art to trick Muzan seeing through Nakime's eye. Worried that Yushiro would take control of her and use the Infinity Castle to their advantage, Muzan activated the curse on Nakime; his act of destroying her cells and killing her subsequently caused the Infinity Castle to grow unstable, eventually emerging from the ground and rupturing from the inside.

Trivia

 * Due to Muzan's favoritism towards them, only the Upper Ranks of the Twelve Kizuki are aware of the castle's existence and have been regularly called to and summoned by Muzan himself to the castle for meetings or new orders. The Lower Ranks in turn have been implied to never have been summoned or let alone know of the castle's existence due to Muzan's own dwindling favor towards them over the centuries due to their constant losses towards the Hashira.