2018/01/31 by Peter Bonventre, Luis Alexandre Pereira, Luís A Pereira
Mathematics · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Context (archaeology) #Equivariant map #Homotopy and Cohomology in Algebraic Topology #Model category #Norm (philosophy) #math.AT
paper · pdf · doi:10.2140/agt.2020.20.2687
published as Algebr. Geom. Topol. 20 (2020) 2687-2778 · Improved exposition in light of the referee's comments
openalex created_date 2018/01/26 · arxiv created 2019/05/03 · openalex publication_date 2020/12/08 · arxiv updated 2021/06/09 · openalex updated_date 2026/08/05
We introduce the analogues of the notions of complete Segal space and of Segal category in the context of equivariant operads with norm maps, and build model categories with these as the fibrant objects. We then show that these model categories are Quillen equivalent to each other and to the model category for [math] – [math] –operads built in a previous paper.\n¶ Moreover, we establish variants of these results for the Blumberg–Hill indexing systems.\n¶ In an appendix, we discuss Reedy categories in the equivariant context.