大般涅槃經義記 1.40

1.40

下明眾生蒙光益中，其中「六趣」舉其所益，謂前光明所照之中六趣眾生皆得益也。人、天、修羅及三惡道為因所向，故名六趣。道別不同，故亦名道。經或說五，離合故爾。六中修羅攝入何道，經論不同。依《毘曇論》，攝入鬼道；依《法念經》，攝入鬼畜，如彼羅睺阿修羅王是師子兒，名為畜生。依《伽陀經》是天、鬼、畜三趣所攝。毘摩之母，天女所生，名之為天，是故經言汝本是天。又復經中名為劣天，今此利分以為六趣。

Below, in clarifying sentient beings receiving the benefit of the light, “the six destinies” therein cites those who were benefited, meaning that among those illuminated by the aforementioned light, sentient beings of the six destinies all attained benefit. Humans, gods, asuras, and the three evil destinies are that toward which cause is directed, hence they are called the six destinies. Because their paths are distinct and not the same, they are also called destinies (gati). The sūtras sometimes speak of five, which is merely a matter of separating or combining. Regarding which destiny the asuras are subsumed under among the six, the sūtras and treatises differ. According to the Abhidharma treatises, they are subsumed under the ghost destiny; according to the Saddharmasmṛtyupasthāna Sūtra, they are subsumed under ghosts and animals—just as that asura king Rāhu is the offspring of a lion and is named an animal. According to the Gāthā Sūtra, they are subsumed under the three destinies of gods, ghosts, and animals. The mother of Vimalacitra was born of a goddess and is named a god, which is why the sūtra says: “You were originally a god.” Furthermore, in the sūtras they are called inferior gods. Now this [sūtra] divides them with sharp distinction into the six destinies.