David Corfield Sweedler Runners for Systems

A draft tutorial on the thesis that Sweedler theory is well-suited to providing a framework for categorical systems theory. It has grown out of LLM chats, and has been influenced by discussions with David Spivak and Maximilien Péroux.

It is in an early stage of development and likely to be modified.

• Introduction
• Part I: Comodels
• Part II: Residual effects
• Part III: Tight direction
• Part IV: Duoidal structure
• Part V: Certification
• Part VI: Cost-enriched
• Part VII: Higher-dimensional execution
• Part VIII: Graph-based systems
• Part IX: Behaviours
• Part X: Smooth systems
• Part XA: Probabilistic systems.
• Part XB: Analytic systems.
• Part XI: Traces
• Part XII: Internal language
• Conclusion
• Appendix A: $IntRun$ via prisms
• Appendix B: Further good regulators
• Appendix C: Quantum runners
• Appendix D: Higher runners
• Arities: Arity-Generated Sweedler Universes from Monoidal Sites