In StarCraft II, the Zerg main base structure is called a Hatchery.
A Hatchery is the basic Zerg structure for establishing a base. It produces Larvae, which are used to create most Zerg units, and it also serves as a drop-off point for gathered resources. Zerg players commonly expand by placing additional Hatcheries at mineral and gas locations.
The Hatchery can be upgraded through the Zerg tech tree. The first upgrade is the Lair, followed by the Hive. These forms provide access to additional technologies and units while retaining the Hatchery’s central role in Zerg economy and production.
The three StarCraft II races use different main-base structures. Protoss players build Nexuses, Terran players build Command Centers, and Zerg players begin with Hatcheries. A Hatchery is therefore not the same thing as a Lair or Hive; those are its upgraded forms.