# Homotopy theory of posets

@article{Raptis2010HomotopyTO,
title={Homotopy theory of posets},
author={George E. Raptis},
journal={Homology, Homotopy and Applications},
year={2010},
volume={12},
pages={211-230}
}
• 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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