correspond with (someone or something)
1. To match or correlate to something. Does this character in the book correspond with one in the movie, or did they eliminate him completely?
2. To communicate with one in a series of messages, typically written ones. When I was a kid, I used to correspond with my sister by writing her letters while she was away at summer camp.
correspond with someone (about someone or something)
and correspond (with someone) about someone or somethingto write letters back and forth with someone about someone or something. I will have to correspond with the manager about that. I corresponded about this with my brother. I corresponded with my brother for over a year. We corresponded about Fred.