There is no evidence that Mahāyāna ever referred to a separate formal school or sect of Buddhism, but rather that it existed as a certain set of ideals, and later doctrines, for bodhisattvas. Initially it was known as Bodhisattvayāna (the "Vehicle of the Bodhisattvas"). Paul Williams has also noted that the Mahāyāna never had nor ever attempted to have a separate Vinaya or ordination lineage from the early schools of Buddhism, and therefore each bhikṣu or bhikṣuṇī adhering to the Mahāyāna formally belonged to an early school. This continues today with the Dharmaguptaka ordination lineage in East Asia, and the Mūlasarvāstivāda ordination lineage in Tibetan Buddhism. Therefore Mahāyāna was never a separate rival sect of the early schools. From Chinese monks visiting India, we now know that both Mahāyāna and non-Mahāyāna monks in India often lived in the same monasteries side by side.
What was the basis of Mahāyāna?
Buddhism