Abstract
Abstract This paper concerns spherical adjunctions of stable $\infty $-categories and their relation to monadic adjunctions. We begin with a proof of the 2/4 property of spherical adjunctions in the setting of stable $\infty $-categories. The proof is based on the description of spherical adjunctions as $4$-periodic semiorthogonal decompositions given by Halpern-Leistner and Shipman [4] and Dyckerhoff et al. [3]. We then describe a class of examples of spherical adjunctions arising from local systems on spheres. The main result of this paper is a characterization of the sphericalness of a monadic adjunctions in terms of properties of the monad. Namely, a monadic adjunction is spherical if and only if the twist functor is an equivalence and commutes with the unit map of the monad. This characterization is inspired by work of Segal [10].
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
