Rectification of enriched ∞–categories

We prove a rectification theorem for enriched 1-categories: if V is a nice monoidal model category, we show that the homotopy theory of 1-categories enriched in V is equivalent to the familiar homotopy theory of categories strictly enriched in V .It follows, for example, that 1-categories enriched in spectra or chain complexes are equivalent to spectral categories and dg-categories.A similar method gives a comparison result for enriched Segal categories, which implies that the homotopy theories of n-categories and .1;n/-categories defined by iterated 1-categorical enrichment are equivalent to those of more familiar versions of these objects.In the latter case we also include a direct comparison with complete n-fold Segal spaces.Along the way we prove a comparison result for fiberwise simplicial localizations potentially of independent use.