Both Uses

correspond
in
Hyperion
(Edited)

He went on a nine-day drunk, awoke in one of the deeper hive tunnels of Lusus with his military cornlog implant stolen-by someone who apparently had taken a correspondence course in surgery-his universal card and farcaster access revoked, and his head exploring new frontiers of pain.†
Part 2 *

correspondence = done from afar
The cybrid was controlled by an AI nexus which corresponds to a security force.†
Part 5 *

corresponds = connects or fits together by being equivalent, proportionate, or matched

Definitions:

(1) (correspond as in: corresponding time period)
connect or fit together by being equivalent, proportionate, or matched

(Two things are equivalent if they have the same or very similar value, purpose, or result.)
(2) (correspond as in: corresponding by email)
communicate -- typically by writing letters or email

A corresponding secretary is an officer of an organization who is responsible for managing the organization's correspondence and keeping a record of it.
(3) (correspondence as in: a correspondence course)
done from afar

For example, a corresponding member or a correspondence course.

This sense of corresponding arose because people who lived in distant cities and could not be present for meetings, could communicate by sending written communications.
(4) (correspondent as in: foreign correspondent of the paper)
a reporter or other representative -- typically from a foreign country or with a particular expertise
(5) (meaning too rare to warrant focus)