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Replacing functors with enriched ones

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arxiv 2210.11320 v3 pith:YHKCV5FE submitted 2022-10-20 math.AT math.CT

classification math.ATmath.CT
keywords describeenrichedpointedbasescorollariescriteriadwyer-kanenrichment
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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.

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