Fernando Abellan and Jonte Gödicke
2026
Abstract.For every adjunction of stable ∞-categories --or more generally, in any locally stable (∞,2)-category-- we give a simple procedure for inverting the twist and cotwist functors associated to this adjunction. As a consequence, we obtain an explicit construction for a left and right adjoint to the inclusion of the (∞,2)-category of spherical adjunctions of stable ∞-categories into all adjunctions. We utilize these adjoints to give a description of the walking spherical adjunction, a locally stable (∞,2)-category which classifies spherical adjunctions, and to provide a synthetic proof of the fact that every spherical functor admits infinitely many left and right adjoints.
