Vigilant - part of speech? [duplicate]

Solution 1:

It’s still an adjective. That’s because remain is intransitive, like be or become or seem. Here’s the relevant sense from the OED:

  1. a. intransitive. With noun or adjectival phrase as complement: to continue to be.

In your example, the predicate complement is an adjectival phrase. Here’s one with a noun phrase as predicate complement:

‘I pass the test,’ she said. ‘I will diminish, and go into the West and remain Galadriel.’

She will remain Galadriel means she will continue to be Galadriel.