Journal
HOMOLOGY HOMOTOPY AND APPLICATIONS
Volume 12, Issue 2, Pages 211-230Publisher
INT PRESS BOSTON, INC
DOI: 10.4310/HHA.2010.v12.n2.a7
Keywords
model category; locally presentable category; poset; small category; Alexandroff space; classifying space
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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 hooked right arrow 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 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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