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A relationship between trees and Kelly–Mac Lane graphs

Published online by Cambridge University Press:  03 July 2006

EUGENIA CHENG
EUGENIA CHENG
Affiliation:
Department of Pure Mathematics, University of Cambridge, Cambridge. e-mail: e.cheng@dpmms.cam.ac.uk
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Abstract

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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 141 , Issue 1 , July 2006 , pp. 33 - 56
Copyright
2006 Cambridge Philosophical Society

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