Weak identity arrows in higher categories

@inproceedings{Kock2005WeakIA,
  title={Weak identity arrows in higher categories},
  author={Joachim Kock},
  year={2005}
}
There are a dozen definitions of weak higher categories, all of which loosen the notion of composition of arrows. A new approach is presented here, where instead the notion of identity arrow is weakened — these are tentatively called fair categories. The approach is simplicial in spirit, but the usual simplicial category D is replaced by a certain ‘fat’ delta of ‘coloured ordinals’, where the degeneracy maps are only up to homotopy. The first part of this exposition is aimed at a broad… 
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