The Gate

The Gate is located under the Kagutsuchi branch of the NOL. In Calamity Trigger, the Sheol Gate serves as both Hakumen and Nu-13 stages. It also serves as Unlimited Ragna's boss stage in score attack mode. It would seem that the Cauldrons of the Library branches and Sector Seven are somehow associated with the gates and could possibly be the door to the gates.

Story
In Calamity Trigger's story, Ragna comes down to the gate after he defeated Jin, presumbly to destroy the Cauldron. There, he encounters Hakumen, forcing him to use his Azure Grimoire to defeat the latter. Noel Vermillion later arrives after the battle to find and arrest Ragna. The Cauldron then appears and she encounters Nu. The two battle, and the fight ends with Nu preparing to kill Noel. However, Ragna arrives and protects Noel from the final blow. He then fights Nu, who ends up stabbing him and taking him with her to the Cauldron to merge. However, Noel saves Ragna, and Nu dies when she falls back into the Cauldron. Rachel then appears and tells Ragna that Noel is the new "eye", who will inherit the true Azure, and that the world will change. She then departs to activate her Tsukuyomi Unit to protect Kagutsuchi from a powerful blast that came from the Nox Nyctores Gigant: Take-Mikazuchi.

As she returns, Hazama appears before the three of them and taunts them, stating that Ragna is too weak for him to fight and only Rachel is able to "keep up" with him.

In Continuum Shift's story, Hakumen is bound to an identical area inside Sector Seven Labs, until Rachel breaks the binding that was placed by Kokonoe. An illusional replication also serves as the battle area where Lambda and Arakune are forced to battle an image of Nu in their respective storylines.

Trivia

 * The word Sheol is pronounced "Sheh-ol" in Hebrew שְׁאוֹל (She'ol), is the "grave", or "pit" or "abyss", indicating that the Sheol gate translates into 'Hell's Gate' or 'Abyss's Gate, and if so, this could imply that the Boundary is actually something akin to Hell.