Matthew, so John said what you probably knew, but hadn't said explicitly, and I was trying to get you to say (!), a monoidal preorder over a discrete poset is just a monoid (thought of in a specific way).

You said

> I see now that not fixing \\(\mathcal{V}\\) is unorthodox. I am sorry, I didn’t intend to defy convention.

I don't care too much about you defying convention, I care a lot more about you being right!

You are trying to define a functor from a category of categories enriched over (all) monoids to the category of groups. I'm not convinced that you have yet defined what the morphisms in your category of enriched categories are. Your functor to the category of groups needs to take morphisms to group homomorphisms.