This is a novel about (on?) integrity

Solution 1:

The key concept here that's creating the dissonance is that you're talking about a novel.

Of course, a more general "book" can be on a topic, with textbooks being the canonical example: a textbook is the definitive work on a subject.

But novels are different. Novels tell a story: they're usually about some people, their circumstances, and the vissictitudes of their lives. That is, novels are narrative, not descriptive.

Of course the subtext or symbology may be a study of a particular topic, which is why you could say a novel is about (in the sense of "circling around") some topic; for the same reason, you could also say "the work is a treatise on ...", or somesuch, where it draws the implications of some behavior or policy.

But it's harder to say the novel, as a book, is on a particular topic, per se.

Solution 2:

Saying that a piece of writing is 'on' something would generally mean the piece is using that thing as a subject.

In your example of 'a novel on etiquette', the novel would likely be about etiquette itself, such as a history of etiquette or a criticism of etiquette.

'A novel about etiquette' may be more likely to feature it as a theme, such as a fictional story about two groups of people, one group who follows the rules of etiquette and another who does not.