Game concept
Duumvirate
The game also links it as Duumvirates, Co-Emperor, Co-Emperors.
From the game's encyclopedia
A Duumvirate is the rule of one Empire by two Characters. A senior emperor (the Liege), and a junior emperor (the Co-Emperor).
They generate passive Influence for both themselves and their senior emperor. How much exactly scales up every 5 years in the job, including any time they spent as Nominal Co-Emperor.
In practice, most power still rests in the hands of the Liege who actually holds the imperial title rather than their Diarch, but the Co-Emperor does have access to several powerful ways to affect the Realm & is a cheaper candidate to promote for Administrative positions.
Notably, Co-Emperors can use the Imperial Expedition Casus Belli at higher levels of Scales of Power swing.
Co-Emperors are able to Usurp their senior emperor via ritually maiming them.
The game's text for patch 1.20.1.2. Words in blue are entries of the encyclopedia: hover one to read it, as in the game.
Duumvirate is an entry of Crusader Kings III's in-game encyclopedia. The game explains it: "A Duumvirate is the rule of one Empire by two Characters." It is part of Co-Rulership. The game also links it as Duumvirates, Co-Emperor and Co-Emperors. Patch 1.20.1.2, from game/common/game_concepts/00_game_concepts.txt and game/localization/english/game_concepts_l_english.yml.
Source: game/common/game_concepts/00_game_concepts.txt, game/localization/english/game_concepts_l_english.yml and the English localisation, Crusader Kings III 1.20.1.2.