I have some questions about the definitions PDF you linked to above, hopefully not too off topic.

Def 12 on monoidal equivalence rubs me strangely, because FG->1 and GF->1 feel like they "want" to be a unit & counit, as from an adjunction, or like a compact category. Except it's a counit & pseudo-counit! What am I to make of this?

Theorem 1, MacLane's theorem - is this similar to how we got a "skeletal" poset out of a preorder by collapsing all the isomorphisms?