Was Adi-Shankara initiated into Kriya Yoga?
The reference of Babaji giving initiation to Adi Shankara is found in Autobiography of a Yogi. As per Paramahansa Yogananda, Mahavatar Babaji himself stated that he gave initiation to Adi Shankara.
Autobiography of a Yogi / Chapter 33 - Babaji, the Yogi-Christ of Modern India:
Babaji’s mission in India has been to assist prophets in carrying out their special dispensations. He thus qualifies for the scriptural classification of Mahavatar (Great Avatar). He has stated that he gave yoga initiation to Shankara, ancient founder of the Swami Order.
Though the initiation was not of Kriya Yoga as mentioned by Paramahansa Yogananda.
Autobiography of a Yogi / Chapter 26 - The Science of Kriya Yoga:
Kriya is an ancient science. Lahiri Mahasaya received it from his guru, Babaji, who rediscovered and clarified the technique after it had been lost in the Dark Ages. "The Kriya Yoga which I am giving to the world through you in this nineteenth century", Babaji told Lahiri Mahasaya, "is a revival of the same science which Krishna gave, millenniums ago, to Arjuna."
From the above, it is clear that Babaji indeed initiated Adi Shankara but not in Kriya Yoga as the knowledge of Kriya Yoga was first given by Babaji to Lahiri Mahasaya and not Adi Shankara.
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