Cave 13 is a small vihara (monastery) that belongs to first century CE. It must have provided accommodations for the monks who presumably would have conducted the rituals in the nearby early Buddhist chaitya halls, Caves 9 and 10. The front of this cave has perished. The hall has seven cells on three sides; each provided with two stone beds, one cell has raised stone pillows as well. The cells are so narrow that it is quite likely that they only served as dormitories (layanagriha). Cave 13, like the four other early Buddhist caves (Caves 9, 10 12, 15A), was refurbished in the Vakataka period; and the remaining traces of the notably “late” red plaster in the cells suggests that here, as in both of the other early Buddhist viharas, this was not done until 477 or later. There is no trace of the cave having ever been painted. 

References:

• Debala Mitra, Ajanta, 1964.
• Walter Spink, Ajanta: A Brief History and Guide, 1990.
• Walter Spink, Volume 18/5 Ajanta: History and Development: Cave By Cave, 2007.