The term simplicial functor is usually used to refer to sSet-enriched functors, hence to simplicially enriched functors, hence to morphisms between simplicially enriched categories.
In principle, but less commonly so in practice, it may also refer to a morphism of simplicial object in Cat. See the discussion at simplicial category.
Another meaning was introduced by Manos Lydakis: simplicial functors are reduced excisive functors from the category of pointed simplicial functors (in the first sense above) from the simplicial category of compact simplicial sets to the simplicial category of simplicial sets. This simplicial category is equipped with a stable model structure that makes it Quillen equivalent to the Bousfield–Friedlander model structure on simplicial spectra?.
See model structure on reduced excisive functors for more information.
Last revised on April 29, 2023 at 09:17:06. See the history of this page for a list of all contributions to it.