In this page http://ncatlab.org/nlab/show/module#InEnrichedCategory, They defined the left module over a monoid object A as an enriched presheaf. However, consider the modules over a ring, the left module should be an $\mathbf{Ab}-$enriched functor. Is it a flaw or there is some reasons.
The same thing happens in http://ncatlab.org/nlab/show/bimodule, They defined the $C-D-$bimodule as a $V-$enriched functor $$C^{\rm op}\otimes D\longrightarrow V$$ However, this is not the case in the usual use of bimoudles over two rings since a $R-S-$bimodule, where $R,S$ are two rings, is actually a $\mathbf{Ab}-$enriched functor $$R\otimes S^{\rm op}\longrightarrow V$$
If this is a flaw, how can I contact them to correct it?