Abstract
We prove a rectification theorem for enriched –categories: if is a nice monoidal model category, we show that the homotopy theory of –categories enriched in is equivalent to the familiar homotopy theory of categories strictly enriched in . It follows, for example, that –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 –categories and –categories defined by iterated –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 –fold Segal spaces. Along the way we prove a comparison result for fiberwise simplicial localizations potentially of independent use.
Citation
Rune Haugseng. "Rectification of enriched $\infty$–categories." Algebr. Geom. Topol. 15 (4) 1931 - 1982, 2015. https://doi.org/10.2140/agt.2015.15.1931
Information