By far the most famous commentary on Nammalwar's Thiruvaimozhi is the Eedu, aka the 36000 Padi, which was composed by the Sri Vaishnava Acharya Vadakku Thiruveedhi Pillai, father of Pillai Lokacharya. Now in the introduction to the Eedu, Vadakku Thiruveedhi Pillai lists 17 schools of Indian philosophy which either reject the Vedas or misinterpret the Vedas in his view. The first 16 are recognizable: the Charvaka school, Jainism, Vaibashika Buddhism, Sautrantika Buddhism, Yogachara Buddhism, Madhyamika Buddhism, the Nyaya school, the Vaisheshika school, the Pashupata Shaivite sect, the Samkhya school, the Yoga school, the Bhatta school of Purva Mimamsa, the Prabhakara school of Purva Mimamsa, Advaita, Aupadhika Bhedabheda, and Svabhavika Bhedabheda. But here is what he says about the 17th one:
These [last three] systems have accepted Brahman as the cause of the creation of the Lord and they accept the Vedas as authoritative. The system of the Ekayana (who accepts Narayana only without Lakshmi to be the Highest) holds that Brahman is associated with certain energies (responsible for creation etc., and not with Lakshmi as the creative energy). And that is its peculiarity.
Thus all these seventeen systems are outside (the authority of) the Vedas, or they have interpreted the Vedas in a wrong manner. And they are all futile.
My question is, what is this Ekayana sect or school criticized by Vadakku Thiruveedhi Pillai? And what were its beliefs?
Was it a Vaishnava sect which believed that Lakshmi was a Jiva as opposed to Paramatma? The Sri Vaishnava sect itself does not have a unified view on this issue; Thenkalais believe Lakshmi is a Jiva (a Nitya Suri to be precise), where Vadakalais believe she is Paramatma just like Vishnu. Now Vadakku Thiruveedhi Pillai lived before the Thenkalai-Vadakalai split, but he seems to have subscribed to the Vadakalai position on Lakshmi. So was he criticizing people who viewed Lakshmi as a Jiva?
Could this have some connection to the Ekayana Shakha of the Shukla Yajur Veda? That is the Shakha associated with the Pancharatra Agamas, which Sri Vaishnavas follow, so it would be odd if Vadakku Thiruveedhi Pillai was criticizing members of the Ekayana Shakha.