The personal lair of the Demon King, Muzan Kibutsuji, in Koyoharu Gotouge's Demon Slayer, the Infinity Castle is a never ending fortress created by the Blood Demon Art of Nakime, a demon in Muzan's employ. Manifesting as a labyrinthine series of rooms, halls, platforms, corridors, and stairs, the space exists beyond the normal confines of space and time. When calling meetings between his most trusted subordinates, namely, the Upper Ranks of the Twelve Kizuki, Muzan generally summons them to the Infinity Castle. However, while the Upper Ranks are well aware of the existence of such a space and know how to traverse its extent, the Lower Ranks have little knowledge of it and were entirely confounded when summoned there after the death of Rui, the Lower Rank Five demon.
Subsequently, appearing in Demon Slayer just prior to the Swordsmith Village Arc, the Infinity Castle was the site for a meeting between the Upper Ranks. Muzan had called the meeting to discuss the matter of Daki and Gyutaro, the Upper Rank Six demons, having been defeated by Tanjiro, Inosuke, Zenitsu, and the Sound Hashira Tengen Uzui at the end of the Entertainment District Arc. Unlike the Lower Ranks, the strongest of Muzan's subordinates seemed quite at home in the Infinity Castle, despite not having been summoned there for over a century. Some members of the Upper Ranks even have dedicated spaces within the castle to themselves, as seen in the case of Kokushibo, who was silently kneeling in a secluded space, far away from the main meeting area, after arriving at the venue before all the others. Although Muzan does not spend all of his time inside the Infinity Castle, it is still his primary base of operations and effective home.
Inside Nakime's Domain
Endless in its extent at first glance, the Infinity Castle seems to have a mind of its own, as evidenced by the fact that its halls, rooms, and corridors appear to be constantly shifting. This state of flux sometimes follows an arbitrary order, but it can be manipulated as required according to the wishes of Nakime, who first formed the extra-dimensional realm with the power of her Blood Demon Art. Nakime can alter the structure, volume, and spatial relationships between different sections of the castle at will, using her biwa to do so. While little has been revealed about her personality and true nature in the anime so far, it is fairly certain that she harbors an intense devotion to Muzan and is loyal to him to a fault, since she has allowed him to use the Infinity Castle as his personal lair.
Nakime can also shift the position and location of any demon or individual inside the Infinity Castle as per her desire, using her biwa to do so. She can also shift and close off passages or open up new ones at a whim, giving her an omnipotence within the domain that is akin to the power of a god. One of the most prominent features of the castle's nature is the absence of any singular source of gravity, as inhabitants can walk on virtually any surface with any orientation — even on the walls and ceilings in certain spaces, or on inverted floors and staircases. Movement in physically impossible directions is also possible throughout the castle, which is just one of the many reasons why Muzan has selected it as his fortress.
The Demon King's Stronghold
For Muzan, the Infinity Castle is sole place of refuge that no member of the Demon Slayer Corps has access to, a sanctuary that only he and Nakime have control over. He can enter and exit the space as he pleases, and make Nakime teleport him between locations throughout the castle, which he does to dramatic effect when addressing the Twelve Kizuki. During the first meeting of the Lower Ranks, where Muzan effectively slaughtered them all save for Enmu, he teleported from a point deep within the castle to a balcony leading outwards with the aid of Nakime. At the time of the Upper Rank meeting, Muzan teleported Gyokko's severed head from the venue for the meeting to the palm of his hand, and then sent it back in an instant.
When summoning and dismissing Muzan's subordinates, Nakime instantly teleports them from their location at the time to the interior of the Infinity Castle, hinting that she can capture anyone she desires so long as she has some idea of their whereabouts. Muzan also made use of this during the final confrontation with the Hashira and the entirety of the Demon Slayer Corps. The majority of this battle took place inside the Infinity Castle, where swarms of demons who were augmented by Muzan to the level of a Lower Rank, were placed under his control to act as foot soldiers to overwhelm the troops of the Demon Slayer Corps.
A Labyrinth Of Horrors
Randomly changing its spatial order at any given moment, with no clear logic in this unstable state, the infinity Castle is a three-dimensional maze-like structure where every inhabitant apart from Muzan and Nakime have to completely surrender to their lack of control. The realm's vast expanse and lack of regard for the traditional laws of physics allows it to host impossible structures, that Nakime can assemble and dismantle on a whim. From hundreds of stories of halls and corridors, to massive indoor gardens and chasms that stretch far beyond what an actual castle could hold. All this was on full display when Akaza, the Upper Rank Three demon of the Twelve Kizuki, fell through the castle's bounds towards the meeting of the Upper Moons.
In effect, it is one of the most potent Blood Demon Arts shown in the series, far exceeding any other technique related to spatial manipulation in Demon Slayer. The sheer extent of the Infinity Castle was put on full display during the opening episode of the Swordsmith Village Arc, providing a taste of what is to come when the final arcs of the manga are adapted by Ufotable for the screen. In the final battle, the Infinity Castle was a major benefit to Muzan in his effort to resist the combined power of the Demon Slayer Corps, providing a last ditch escape for him in desperate times. With the quality of animation that has been on show at every point in the anime so far, it is highly likely that they will do justice to this mysterious, alluring space, pushing the visual experience of traversing it to even greater heights than before.