Spherical Monadic Adjunctions of Stable Infinity Categories

Abstract This paper concerns spherical adjunctions of stable $\infty $-categories and their relation to monadic adjunctions. We begin with a proof the 2/4 property in setting $-categories. The is based on description as $4$-periodic semiorthogonal decompositions given by Halpern-Leistner Shipman [4] Dyckerhoff et al. [3]. then describe class examples arising from local systems spheres. main result this characterization sphericalness terms properties monad. Namely, adjunction if only twist functor an equivalence commutes unit map inspired work Segal [10].