Replacing functors with enriched ones
arXiv:2210.11320
Abstract
We describe simple criteria under which a given functor is naturally equivalent to an enriched one. We do this for several bases of enrichment, namely (pointed) simplicial sets, (pointed) topological spaces and orthogonal spectra. We also describe a few corollaries, such as a new proof of a result of Lurie on Dwyer-Kan localizations.
49 pages. v3: updated references, added Section 5.2. v2: Simplified proof of main result of section 5 and fixed some minor details. Comments welcome!