As the Minister bids you welcome into his den of devilry, he brings along with him an essential gameplay mechanic in the Megami Tensei franchise -- fusion. Using the Cathedral's inexplicable power, he can often fuse up to three demons at a time, but never one higher than the protagonist's current level. As he admits, the fusion process is not perfect and sometimes unfortunate accidents may occur. In the Devil Summoner series, the Cathedral of Shadows is replaced with the analogous Goumaden, while the Persona series uses the also similar Velvet Room.
In the Devil Survivor series and Shin Megami Tensei IV, the Cathedral of Shadows appears as an application within the main characters' COMPs. The Minister appears in IV's Cathedral as a disembodied, voxelized head.