Homotopy theory of posets

  title={Homotopy theory of posets},
  author={George E. Raptis},
  journal={Homology, Homotopy and Applications},
  • G. Raptis
  • Published 2010
  • Mathematics
  • Homology, Homotopy and Applications
This paper studies the category of posets Pos as a model for the homotopy theory of spaces. We prove that: (i) Pos admits a (cofibrantly generated and proper) model structure and the inclusion functor Pos ↪→ Cat into Thomason’s model category is a right Quillen equivalence, and (ii) there is a proper class of different choices of cofibrations for a model structure on Pos or Cat where the weak equivalences are defined by the nerve functor. We also discuss the homotopy theory of posets from the… 
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