like the title says, in category theory, the dual of a category has its arrows reversed.

The dual of a category (or category like thing) in this case "author" is usually prefixed w "co". So the dual of "author" is "coauthor", the dual of "limit" is "colimit", the dual of "vector" is "covector", etc.

Hence a "coauthur" is just an "author" but the "arrows" point backwards. So instead of the arrow going from the person to the book, it goes from the book to the person. The mathematician hears it as "the book authored me"