What is the functionality of a cathedral in the Diablo world?

A cathedral is a Christian church which contains the seat of a bishop in the real world. While there is a bishop in the Diablo universe there doesn't seem to be any kind of organized religion in the Diablo universe (at least in the games). Since there is no organized religion there shouldn't be any bishops or cathedrals in that universe. There is also a priest and a chapel in Wortham in the 1st Act of Diablo 3. But again, no religion is ever mentioned in the games, and no religion is seemed to be fallowed in the Sanctuary world.

To whom (or what) is the cathedral dedicated, and what religion is practiced in it?

Solution 1:

Here is some of the Plot from the Diablo Wiki describing the cathedral and monastery.

The setting of Diablo includes the world of Sanctuary, as well as Heaven and Hell. After eons of war between angels and demons, the ascension of man prompted the three Lords of Hell (including Diablo himself) to seek victory through influence, prompting their exile into the mortal realm. There, they sowed chaos, distrust, and hatred among the humans of Sanctuary until a group of magi trapped them in soulstones. Diablo's soulstone was buried deep in the earth and a monastery was built over the site.

Generations passed and the purpose of the monastery was forgotten. A small town named Tristram sprang up next to the monastery's ruins. When King Leoric rebuilt the monastery as a cathedral, Diablo manipulated its archbishop to destroy his soulstone prison. Diablo subsequently possessed the king, sending out his knights and priests to battle against peaceful kingdoms, and then possessed the king's son, filling the caves and catacombs beneath the cathedral with creatures formed from the young boy's nightmares.

Tristram became a town of fear and horror, where people were abducted in the night. With no king, no law, and no army left to defend them, many villagers fled.

Small timeline (taken from here):

• 1262: King Leoric and Archbishop Lazarus come to the town and remake the old monastery into a Zakarum church.
• 1263: The events of Diablo I.
• 1264: The rogues of the Sisterhood of the Sightless Eye are forced
  out of their monastery and corrupted by Andariel, who is subsequently slain.

One more regarding the Cathedral itself, and the Religion:

Tristram's Cathedral is an ancient Horadrim edifice. Under it, they imprisoned Diablo in his soulstone. When the Horadrim faded away, the cathedral is left as decrepit ruin. When the Zakarum came to be the most practiced religion, the Cathedral became a place of worship and the seat of King Leoric, who converted Khanduras to the Zakarum religion.

To summarize it: The monastery was 'dedicated' to keep Diablo in his prison. King Leoric rebuilt the monastery into the cathedral, and Diablo manipulated the archbishop to release him from his prison. The capital of Khanduras, Tristram, took Zakarum as a religion.

Other sources: http://www.diablowiki.com/Archbishop_Lazarus_%28Diablo_I%29

Solution 2:

There are two known major religions in the Diablo world (from the D3 lore):

• The Temple of the Triune; in reality Diablo, Mephisto & Baal in disguise
• The Cathedral of Light, set up by the rogue archangel Inarius to counter the Triune.

Some of the orders such as Zakarum are sects or splinter groups following the Cathedral of Light. Since the disappearance of the Prophet (Inarius was captured and tortured in Hell), the cathedral of light devolved into various factions while the Triune also underwent a decline (as the Prime Evils were captured in soulstones).

There are also some others like the Witch Doctor religion that don't follow either of these two, but appear to be less widespread through Sanctuary.

It is never stated which one the Tristram cathedral belonged to (possibly the Light side, since its known as a 'cathedral' not a 'temple'), but it should be used for the worship of one of these two religions (or their derivatives).

so a priest and a chapel in Wortham in the 1st Act of Diablo 3.

There is no actual indication of which one, similar to Tristram's grander structure. However, its apparent that this is a very low level place of worship; with no guards or inquisitors around. If we assume the parallel in naming with our world, chapel would indicate a relation to the cathedral.

Solution 3:

Philosophical point, but is it still a religion without a need for belief?

Philosophy aside, the realities portrayed in Diablo include a very real and obvious state of the realms of Heaven and Hell. People may still worship the beings in Heaven (or Hell for that matter) and there is still a need for buildings to facilitate this but there's no real need to name it when there is no need to differentiate between a cathedral built for one religion or another.

In short, there is no name mentioned in any of the games and no real need for one either. I imagine most of the roles and buildings serve much the same purpose as the Catholic/Christian equivalents.