Tripitaka is taught to and learned by monks in the monasteries and laypeople are encouraged to learn. From a Tibetan viewpoint, the texts H.H. quoted are included within one of the three baskets. Shantideva's Bodhisattvacharyavatara is included in the Sutra Pitaka (although it is not a sutra), Asanga's Mahāyāna Sūtrālamkāra kārikā is included in the Abhidharma Pitaka, Kamalashila's Stages of Meditation belongs to the Abhidharma Pitaka, Nagarjuna's Karika belongs to the Abhidharma Pitaka as well, and so forth.
In the ninth chapter of the Bodhisattva Deeds, Shantideva explains that anything that is included within one of the three baskets was the speech – or at least the intention – of Lord Buddha. His Holiness the Dalaï-Lama highlighted this principle. In Illuminating the Path to Enlightenment, he writes:
As Dromtönpa lay dying, his head rested on the lap of one of his chief
disciples, Potowa, and he noticed that Potowa was crying. Then Potowa
said, “After you pass away, in whom can we entrust our spiritual
well-being? Who can we take as our teacher?” Dromtönpa replied, “Don’t
worry. You’ll still have a teacher after I’m gone—the tripitaka, the
threefold collection of the teachings of the Buddha. Entrust yourself
to the tripitaka; take the tripitaka as your teacher.”
Furthermore, in 'Transcendent Wisdom', His Holiness writes:
The three baskets are (1) Vinaya, dealing with moral discipline; (2)
Sutra, dealing with the training in meditative concentration and other
facets of the path of awakening; and (3) Abhidharma (sometimes
translated as "higher knowledge"), concerning a diversity of topics
ranging from psychology to cosmology. For a further explanation see
Opening the Eye of New Awareness, pp. 47-52.
We hold that the Tibetan translators showed to which basket the text they were translating belonged, by way of paying particular homage. As His Holiness writes in his commentary to Stages of Meditation:
The intention [of the Tibetan translator paying homage when
translating Nagarjuna and so forth] was to cearly indicate to which of
the three divisions [the pitakas, or baskets] of the Buddha's
teachings any sutra or commentary belongs. [It goes as follows:]
1. Supplication is made to all Buddhas and Bodhisattvas if a text belongs to the Collection of Discourses [i.e. Sutra Pitaka].
2. And if a text belongs to the Collection of Knowledge [i.e. Abhidharma Pitaka], supplication is made to Manjushri.
3. In order to indicate that a certain text belongs to the Collection of Discipline [I..e Vinaya Pitaka], supplication is made to the