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 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, Shipman and by Dyckerhoff, Kapranov, Schechtman, Soibelman. 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 Ed Segal.

43 pages, final version

References in corpus (5)

• Higher Topos Theory
• Stable Infinity Categories
• Cyclic structures and broken cycles
• Ginzburg algebras of triangulated surfaces and perverse schobers
• Spherical adjunctions of stable $\infty$-categories and the relative S-construction

Cited by in corpus (2)

• Ginzburg algebras of triangulated surfaces and perverse schobers
• Spherical adjunctions of stable $\infty$-categories and the relative S-construction