Coend Optics for Quantum Combs

@article{Hefford2022CoendOF,
  title={Coend Optics for Quantum Combs},
  author={James Hefford and Cole Comfort},
  journal={ArXiv},
  year={2022},
  volume={abs/2205.09027}
}
We compare two possible ways of defining a category of 1-combs, the first intensionally as coend optics and the second extensionally as a quotient by the operational behaviour of 1-combs on lower-order maps. We show that there is a full and bijective on objects functor quotienting the intensional definition to the extensional one and give some sufficient conditions for this functor to be an isomorphism of categories. We also show how the constructions for 1-combs can be extended to produce… 
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