The Parallel Full Approximation Scheme in Space and Time (PFASST) is a time-parallel iterative method, which already shows promising results for many use cases. However, a solid and reliable mathematical foundation is still missing. In this talk, we deconstruct PFASST into its building blocks and explore the strong connection between PFASST and classical multigrid schemes. We show that the PFASST algorithm for linear problems can be conveniently and rigorously described as a multigrid-in-time. Since multigrid methods where studied extensively in the past, a lot can be gained from this connection for a better understanding of PFASST. We focus on the application of Local Fourier Mode Analysis and show first results.