The Cathedral of Syndetic Ascension is the tower in Problem Sleuth which connects the two halves of the imaginary universe, the Imaginary City and the four kingdoms. It also connects to Mobster Kingpin's Chicago Overcoat. It is arguably the largest building in the game. It has various beasts and creatures inside. It is interesting to note that the Cathedral has an undefined height, as it took Problem Sleuth and the two Ace Dicks only 5 levels to ascend. On the other end, it is an incredible 66,666 floors for The Four Warriors. This is because Problem Sleuth and the two Ace Dicks entered the Cathedral in the material plane (through the Speakeasy) and ended up closer to the middle, while the Four Heroes entered it in the imaginary universe, as stated by Andrew Hussie, and started from the bottom/top.