Weak complicial sets I. Basic homotopy theory

@article{Verity2008WeakCS,
  title={Weak complicial sets I. Basic homotopy theory},
  author={Dominic R. Verity},
  journal={Advances in Mathematics},
  year={2008},
  volume={219},
  pages={1081-1149}
}
This paper develops the foundations of a simplicial theory of weak ?-categories, which builds upon the insights originally expounded by Ross Street in his 1987 paper on oriented simplices. The resulting theory of weak complicial sets provides a common generalisation of the theories of (strict) ?-categories, Kan complexes and Joyal's quasi-categories. We generalise a number of results due to the current author with regard to complicial sets and strict ?-categories to provide an armoury of well… Expand

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