Resolutions of singularities are a key idea in birational algebraic geometry. Resolutions are important as they allow one to find, for a singular scheme, a non-singular scheme in the same birational class. Resolutions have been studied extensively in classical algebraic geometry, but are not as well understood in the derived category setting. In this thesis we extend recent results for computing crepant categorical resolutions and their kernels in the A1 and A2 cases to the arbitrary An case.
