co-author vs author

co-author is not a noun while author is a noun.

Word	Noun	Adjective	Verb	Adverb
co-author	No	No	Yes	No
author	Yes	No	Yes	No

As verbs, author is a hypernym of co-author; that is, author is a word with a broader meaning than co-author:

co-author (noun)	author (noun)
	writes (books or stories or articles or the like) professionally (for pay)
	someone who originates or causes or initiates something

co-author (verb)	author (verb)
be a co-author on (a book, a paper)	be the author of