A discrete homotopy theory for binary reflexive structures

@article{Larose2004ADH,
  title={A discrete homotopy theory for binary reflexive structures},
  author={B. Larose and Claude Tardif},
  journal={Advances in Mathematics},
  year={2004},
  volume={189},
  pages={268-300}
}
Abstract We present a simple combinatorial construction of a sequence of functors σ k from the category of pointed binary reflexive structures to the category of groups. We prove that if the relational structure is a poset P then the groups are (naturally) isomorphic to the homotopy groups of P when viewed as a topological space with the topology of ideals, or equivalently, to the homotopy groups of the simplicial complex associated to P . We deduce that the group σ k ( X , x 0 ) of the pointed… Expand
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