>A good category theorist knows lots of systematical ways to find good definitions, which convert "magic" to "method".

John, could you please recommend some paper/book/blog as a good introduction to such systematical methods?
Progressing so far through the book/course already brought a lot of value, but conditions like this one for monoidal preorders make me feel uneasy. Handwavingly I knew that this is just another monotonicity condition, but why exactly this one, and how the form to express it was chosen? - questions like this bothered me this week. It's looks like some intuition was lost while trying to find the most concise representation of the structure of a monoidal product.