Thomas Blom: Postdoc day, Seminar 4: Replacing functors by enriched ones

Abstract: When studying homotopy theory in an enriched setting, e.g., in an enriched model category, one may wonder when a functor between underlying categories is equivalent to an enriched one. I will discuss conditions under which this is possible for several bases of enrichment, including simplicial sets, topological spaces and various models of spectra, and illustrate these with examples. Finally, I will discuss my own motivation for studying this question; namely, that it can be used to tackle certain problems appearing in Goodwillie's calculus of functors.