Cohorts are NPC's. (Page 104 of the DMG)
The DM controls NPC's. (I have no idea where this is stated, but I guarantee its truth)
DMG pg 106
A cohort is effectively another PC in the party under that player's control. . .
PHB pg 311
nonplayer character (NPC): A character controlled by the
Dungeon Master rather than by one of the other players in a game
session, as opposed to a player character.