According to “The good grammar” by Swan and Walter.
My, your, his, her, our, your, their
Are possessive pronouns.
According to Cambridge dictionary they are determiners.
Now how can those words can be both determiners (part of speech: adjectives) and personal pronoun (part of speech: personal pronoun)
Language Log on determiners and adjectives. It's not specifically about pronouns, but it illustrates that there's different terminology when it comes to language.
Andrew, what you say is correct, part of speech is all about the function of a word, not the word itself.
Only If I check in a dictionary for a word, I am supplied with the various functions this word can have. But the thing is, as far as my dictionaries, only one part of speech is stated...
So would a determinative possessive pronoun be considered a determinant or an adjective, or both at the same time?