Opetopes and chain complexes

Richard Steiner

We give a simple algebraic description of opetopes in terms of chain complexes, and we show how this description is related to combinatorial descriptions in terms of treelike structures. More generally, we show that the chain complexes associated to higher categories generate graphlike structures. The algebraic description gives a relationship between the opetopic approach and other approaches to higher category theory. It also gives an easy way to calculate the sources and targets of opetopes.

Keywords: opetope; augmented directed complex

2010 MSC: 18D05

Theory and Applications of Categories, Vol. 26, 2012, No. 19, pp 501-519.

Published 2012-09-19.


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