2023/02/08 by Tim Campion, Campion, Tim · 1 citation
Mathematics · #18N60 (Secondary) #55M05 (Primary) 18M15 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2302.04207
openalex publication_date 2023/02/08 · openalex created_date 2023/02/11 · openalex updated_date 2026/07/28
We study the left adjoint \mathbbD to the forgetful functor from the ∞-category of symmetric monoidal ∞-categories with duals and finite colimits to the ∞-category of symmetric monoidal ∞-categories with finite colimits, and related free constructions. The main result is that \mathbbD \mathcal C always splits as the product of 3 factors, each characterized by a certain universal property. As an application, we show that, for any compact Lie group G, the ∞-category of genuine G-spectra is obtained from the ∞-category of Bredon (a.k.a ``naive") G-spectra by freely adjoining duals for compact objects, while respecting colimits.