I will then present the abstract framework and sketch how it relates to other, similar formalisms, emphasizing its strengths and limitations. After that, I will briefly discuss our recent work on applying the formalism in the context of the Poincaré group, and how this setup can be seen as a first step towards a novel, relational, and operational foundation for quantum field theory. Finally, I will outline how I envision extending the formalism to include spinor fields, gauge theories, curved spacetimes, and perhaps even indefinite geometries. I believe such extensions are feasible thanks to recently established mathematical results, which I will mention towards the end of the talk if time permits. My hope is to spark interesting questions, objections, and critiques.