I will speak about adjacent weight and t-structures (this means that either left or ‘right hand side halves’ of these ‘structures’ w and t coincide) in triangulated categories. In particular, for any compactly generated t there exists a weight structure w right adjacent to it. This yields injective cogenerators for the heart of t; it follows that the heart of t is Grothendieck abelian. To construct this w I proved that any perfect set of objects (in a smashing triangulated category) generates a weight structure w. Moreover, if a triangulated category satisfies the Brown representability property then t that is left adjacent to w exists if and only if w is smashing (i.e., coproducts respect weight decompositions).
This video is part of the New Directions in Group Theory and Triangulated Categories seminar series.
