The Cathedral of Causality is the home of Deus Ex Machina and Muru Muru. It is depicted as a large domed building with an interior with purple and pink tint.
Described as an imaginary place, the Cathedral can be accessed by anyone who knows of it. Yukiteru Amano visited it several times, and Minene Uryu visited at least once.
The Cathedral appears to be tied to Deus's existence, as it noticeably crumbles as his life reaches its end. It is also affected by changes in the timeline, as it was almost destroyed when Yukiteru changed the future by seeing the dead bodies in Yuno's house.