The Monadic Tower for $\infty$-Categories

Abstract

Every right adjoint functor between presentable ∞-categories is shown to decompose canonically as a coreflection, followed by, possibly transfinitely many, monadic functors. Furthermore, the coreflection part is given a presentation in terms of a functorial iterated colimit. Background material, examples, and the relation to homology localization and completion are discussed as well.Weltchronik in Versen, Szene: Der Turmbau zu Babel (c. 1370s). Depiction of the construction of the tower of Babel.