Flat vs. filtered colimits in the enriched context

The importance of accessible categories has been widely recognized; they can be described as those freely generated in some precise sense by a small set objects and, because that, satisfy many good properties. More specifically finitely characterized as: (a) free cocompletions under filtered colimits, and (b) flat presheaves on category. equivalence between is what makes the theory so general fruitful. Notions enriched accessibility have also considered literature for various bases enrichment, such Ab,SSet,Cat Met. problem this context that no longer true general. aim paper then to: give sufficient conditions V ? holds; holds up to Cauchy completion; explore examples not covered (1) or (2).