Abelian categories and triangulated categories provide fundamental frameworks to study homological and cohomological problems across algebraic geometry, topology and representation theory. In this talk we will explain how we can study the 2-category AbCat of abelian categories and the...

We present a monadic approach to actions of internal categories and connect it with a categorical formulation of Galois descent. Actions of internal categories are shown to a certain type of monad, while Galois descent is characterized as effective descent together with a pseudo-torsor...