Monadicity, purity, and descent equivalence

Abstract

This dissertation is intended to study monadicity, to introduce the notion of descent equivalence, and to initiate descent theory in locally presentable categories. At first, we give two monadicity results which do not involve explicitly checking preservation of certain coequalizer diagrams, as well as a type of “monadicity lifting” theorem. Then we summarize the fundamentals of descent theory in order to lay the groundwork for developing the new notion of descent equivalence and for investigating its properties. Finally, we study closedness of (effective) codescent morphisms under directed colimits and their connection with pure monomorphisms in locally presentable categories.