This paper studies the category of posets $mathcal{Pos}$ as a model for the homotopy theory of spaces. We prove that: (i) $mathcal{Pos}$ admits a (cofibrantly generated and proper) model structure and the inclusion functor $mathcal{Pos o Cat}$ 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 $mathcal{Pos}$ or $mathcal{Cat}$ where the weak equivalences are defined by the nerve functor. We also discuss the homotopy theory of posets from the viewpoint of Alexandroff $T_0$-spaces, and we apply a result of McCord to give a new proof of the classification theorems of Moerdijk and Weiss in the case of posets.
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