Lukas Bonfert, Max-Planck Institut für Mathematik Bonn
Orthogonality of weight and t-structures via derived projective covers

Abstract: Weight structures (also known as co-t-structures) and t-structures on triangulated categories are closely related by orthogonality. The characterization of orthogonality in terms of simple-minded collections and silting collections is very similar to the relation of the indecomposable projectives to the simple objects in an abelian category. I will explain how this can be formalized using derived projective covers, which are an analog of projective covers for triangulated categories. I will also discuss a result about Koszul duality between simple-minded and silting collections, which is a first step towards understanding the (conjectural) Koszul duality between weight structures and t-structures. The talk is based on arXiv:2309.00554.