The Goddess Cathedral is the unique faction structure for the Kingdom of Hyrule. It provides a massive bonus to conversion and religious order. A Goddess Cathedral costs 5000 rupees and requires at least a City-level settlement to construct.
The Golden Goddesses of Hyrule are at the very least acknowledged by many in Hyrule. Unfortunately this is still unacceptable to the Hylians: their law mandates that all must worship the Goddesses. These cathedrals can be construction in any city controlled by the Kingdom of Hyrule to spread the faith of the Triforce.