- For every functor we have the implications
is very rich is rich (Hilton) is opaque is consistent (Frei)
and each converse implication is false in general.
- An opaque functor is consistent and co-consistent (i.e. is consistent).
- If is an adjunction, is opaque if and only if is opaque.
- If is an adjunction, is very rich if and only if it is rich, if and only if it is opaque, if and only if it is consistent.