The Gate

The Gate is located under the 13th Hierarchical City "Kagutsuchi" branch of the World Void Information Controlling Organization. In BlazBlue: Calamity Trigger, the Sheol Gate serves as both Hakumen and Nu -No. 13- stages. It also serves as Unlimited Ragna the Bloodedge's boss stage in score attack mode. It would seem that the Kilns of the Library branches and Seventh Agency are somehow associated with the gates and could possibly be the door to the gates.

Story
In BlazBlue: Calamity Trigger's story, Ragna comes down to the gate after he defeated Jin Kisaragi, presumbly to destroy the Kiln. There, he encounters Hakumen, forcing him to use his Blue Grimoire to defeat the latter. Noel Vermillion later arrives after the battle to find and arrest Ragna. The Kiln 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 Kiln to merge. However, Noel saves Ragna, and Nu dies when she falls back into the Kiln. Rachel Alucard then appears and tells Ragna that Noel is the new "eye", who will inherit the true Blue, 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 Arch-Enemy, Highlander: Takemikazuchi.

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 BlazBlue: Continuum Shift's story, Hakumen is bound to an identical area inside Seventh Agency labs, until Rachel breaks the binding that was placed by Kokonoe. An illusional replication also serves as the battle area where Lambda -No. 11- 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' Gate.