Origin: Latin suffix -al
Cathedral has 5 different meanings across 2 categories:
any large and important church
"The tourists gathered outside the cathedral to admire its towering spires."
A big church building, central place for some area.
"The Gothic cathedral stands as a magnificent central landmark in the heart of the city."
In plain English: A cathedral is a very large and important church that serves as the main worship place for a bishop's area.
"We walked through the busy city streets until we reached the beautiful cathedral in the town square."
relating to or containing or issuing from a bishop's office or throne
"a cathedral church"
Relating to the throne or the see of a bishop.
"The cathedral served as the official seat where the bishop held his throne and administered his diocese."
In plain English: The adjective form of cathedral does not exist because a cathedral is always a noun referring to a large church building.
"The cathedral square is now used for weekend markets and street performances."
Usage: Use this adjective only when referring specifically to things connected with a bishop's official seat or authority, such as cathedral courts or cathedrals in legal contexts. Do not use it simply because something is located inside a large church building; that describes the noun form instead.
The word cathedral comes from the Latin cathedrālis, which is derived from cathedra meaning "throne" or "seat." It entered English via Old French and Middle English to describe a church built around the bishop's chair.