What is it called when an author dedicates a work to another author?

Usually the person who has a book dedicated to them from the author is a friend, family member, or someone who helped a great deal to write the book. The person could have critiqued the book, shared ideas, etc. The author appreciates this, and therefore, dedicates the book to he person.

Not all authors dedicate their books, but some have an 'acknowledge page' at the beginning or end of their book where they thank everyone who was involved in writing the book.

Sometimes the author will thank even people who provided music for them, like William P. Young, the author of 'The Shack'. William P. Young thanks everyone who helped him in his quest, and even thanks songwriters.