The Cathedral is a locus of power according to neo-reactionary theory. A good summary of the concept is on the Canis Society wiki which defines Cathedral as "powerful institutions, typically the press and academia, which direct a society's cultural and policy-setting behavior."
The "Cathedral" does not refer to an organized conspiracy, rather a distributed network of opinion shapers who typically advance left-wing views and internationalism. The closest IDW equivalent term is the DISK
The Cathedral originated from dissident-right blogger Mencious Moldbug, referring not to any self-aware process, but rather, "spontaneous coordination" on the part of culture-setters who constitute a priestly class. They set a "Synopsis," a set of doctrines. The Cathedral is sometimes described as a political machine.