Francesco Genovese, Charles University Prague

Title: Derived injective objects and some applications

Abstract: The importance of injective objects and injective resolutions in abelian categories cannot be underestimated. In the higher categorical / derived framework, abelian categories are replaced by (enhanced) triangulated categories endowed with a t-structure. That setup allows to define a higher version of the injective objects, namely the derived injectives. In this talk I will show how to use such derived injectives to build suitable resolutions of objects in terms of particular twisted complexes; moreover, I will show how they help us to give a proof of a “derived Gabriel-Popescu theorem” involving t-structures.