Cloister:
"A cloister (from Latin claustrum, "enclosure") is a rectangular open
space surrounded by covered walks or open galleries, with open arcades
on the inner side, running along the walls of buildings and forming a
quadrangle or garth. The attachment of a cloister to a cathedral or
church, ... usually indicates that it is (or once was) part of a
monastic foundation.." -
Wikipedia .