Infinity Castle

The Infinity Castle is 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.

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, Sanemi, and Gyomei 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.

Layout
The Infinity Castle is an endlessly large extra-dimensional space of wooden rooms, endless halls, and moving corridors. It possesses a warped direction of gravity, allowing demons to stand upright, upside down, or perpendicularly on the walls, or move in physically impossible directions. Its unusual structure and layout as Nakime's Blood Demon Art allows any structure within to shift at her will.

Using her biwa, she can manipulate the position of any demon inside and take them to any location in her range. During the conclusion of the Lower Ranks meeting, Nakime teleported Muzan to a balcony leading outside despite his original position being deep within the castle; moreover, the doors she used to close around him all seem to constantly shift within the unusual gravity, spinning within themselves as she changes its layout.

The Infinity Castle's range seems to extend beyond its already incomprehensibly large area, as Nakime was able to manipulate Enmu and take him to an unknown town seemingly nowhere close to the castle, even dropping him in place using a supernatural vanishing door. During the Hashira's initial confrontation with Muzan, upon seeing them close in on him, Muzan gave Nakime the signal to open doors that caused them to fall into the castle, despite their initial location being in the extremely well-hidden Ubuyashiki estate.

Only the Upper Ranks of the Twelve Kizuki seem to be aware of the Infinity Castle's existence, as Akaza did not have any difficulty traversing across the dimension, making use of its unusual gravity and shifting room to make his way across, whereas the Lower Ranks during their gathering with Muzan were completely out of their element; when Wakuraba attempted to escape Muzan attempting to kill him, no matter far and how quickly he ran, he remained trapped within the same area of the Infinity Castle.

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.