Both times it was like: we define it this way in this paper. I didn't get the feeling it was a general usage thing. The definitions given were plenty rigorous,

Both times it was like: we define it this way in this paper. I didn't get the feeling it was a general usage thing. The definitions given were plenty rigorous, it's just that there weren't any other morphisms lying around that the author needed to disambiguate between. "Equivalence" would've done just as well. I think the humanities are important, I just think it would be a better PR move to resist the urge to style them after anything else.