Replacing functors with enriched ones
Algebraic Topology
2025-08-20 v3 Category Theory
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.
Cite
@article{arxiv.2210.11320,
title = {Replacing functors with enriched ones},
author = {Thomas Blom},
journal= {arXiv preprint arXiv:2210.11320},
year = {2025}
}
Comments
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!