Categorical absorption of singularities

Resolution of singularities from the categorical point of view is an operation that replaces the derived category of a singular variety by a bigger smooth and proper triangulated category. Absorption of singularities, on a contrary, replaces the derived category of a singular variety by a smaller smooth and proper triangulated category. In the talk I will introduce P-infinity objects and show how they can be used to absorb singularities of nodal varieties.