The 「って」 + 「いい」 in this sentence what does it mean?

Question

This is piece of dialogue from a book, and i don't quite get what the 「って」 is doing, if it's a quote, i don't get why they would need to phrase it as a quote. I'm guessing the 「いい」 is the word for "good"

「異世界に行かない？　一つだけ好きな物を持っている って いいわよ。」

I can guess the the full sentence is something like "you are allowed to take only 1 item you like with you" since the previous was "won't you go to another world?" from context but i want to know what the 「って」 and 「いい」 are for.

Answer 1

As your sentence is 持って行っていい.

していい means "be allowed to".

持っていっ is a euphonic change of 持っていき, which is 連用形(te-form) of 持っていく.