A relationship between trees and Kelly–Mac Lane graphs

@article{Cheng2006ARB,
  title={A relationship between trees and Kelly–Mac Lane graphs},
  author={Eugenia Cheng},
  journal={Mathematical Proceedings of the Cambridge Philosophical Society},
  year={2006},
  volume={141},
  pages={33 - 56}
}
  • Eugenia Cheng
  • Published 2006
  • Mathematics
  • Mathematical Proceedings of the Cambridge Philosophical Society
We give a precise description of combed trees in terms of Kelly–Mac Lane graphs. We show that any combed tree is uniquely expressed as an allowable Kelly–Mac Lane graph of a certain shape. Conversely, we show that any such Kelly–Mac Lane graph uniquely defines a combed tree. We show how to apply this to the construction of opetopes. 
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