Rectification of enriched infinity-categories
Research output: Contribution to journal › Journal article › Research › peer-review
We prove a rectification theorem for enriched infinity-categories: If V is a nice monoidal model category, we show that the homotopy theory of infinity-categories enriched in V is equivalent to the familiar homotopy theory of categories strictly enriched in V. It follows, for example, that infinity-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 (infinity,n)-categories defined by iterated infinity-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 fibrewise simplicial localizations potentially of independent use.
Original language | English |
---|---|
Journal | Algebraic & Geometric Topology |
Volume | 15 |
Pages (from-to) | 1931–1982 |
ISSN | 1472-2747 |
DOIs | |
Publication status | Published - 2015 |
Externally published | Yes |
- math.AT, math.CT, 18D20, 18D50, 55P48, 55U35
Research areas
ID: 145773352