The study of higher-order quantum transformations has seen great interest over the last 10 years. They allow for the information-theoretic study of phenomena such as indefinite causal order that are expected to be present in a full-blown theory of quantum gravity, and they are known to provide advantage in certain computational and communication tasks. I will give an introduction to this field before discussing the current categorical methods employed to model quantum supermaps in terms of strong profunctors. By combining a series of canonical constructions I will show how it is possible to build a BV-category which supports higher-order quantum theory and provides logical connectives describing the arrangements of agents in spacetime. This is based on joint work with Matt Wilson.