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In this paper we study derived categories of nodal singularities. We showthat for all nodal singularities there is a categorical resolution whose kernelis generated by a $2$ or $3$-spherical object, depending on the dimension. Weapply this result to the case of nodal cubic fourfolds, where we describe thekernel generator of the categorical resolution as an object in the boundedderived category of the associated degree six K3 surface.  This paper originated from one of the problem sessions at the InteractiveWorkshop and Hausdorff School "Hyperk\"ahler Geometry", Bonn, September 6-10,2021.

Kernels of categorical resolutions of nodal singularities