I always thought so too. Maybe we both are wrong.
A monastery is the habitation of monks, derived from the Greek word for a hermit's cell. Western Christian monasteries are also called abbey, priory, charterhouse, friary, and preceptory, while the habitation of nuns can also be called a convent. The communal life of a monastery is called cenobitic, as opposed to the anchoretic (or anchoritic) life of an hermit.
From Wikidedia