?? "co-r-module object in _s-module_" .... ??? not-so-subtly different interpretations of this ... ???? ....

?? ab-gp-enriched functor from r to _s-module_^op ... ?? ess just r^op-module ...

?? vs ... product-preserving functor from _free fg r-module_^op to _s-module_^op ...

?? hmmm, or _are_ these the same ??? ...

?? some other distinction that i was groping for here ?? .... ???? ...

?? "toric" situations ... ?? where some such distinction might cause confusion ... ??? ....