Geodesic
Homotopy theory of posets
Homology, homotopy, and applications, Tome 12 (2010) no. 2, pp. 211-230.

Voir la notice de l'article provenant de la source International Press of Boston

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 $\mathcal{Pos \to Cat}$ 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.
DOI : 10.4310/HHA.2010.v12.n2.a7
Classification : 18B35, 18G55, 54G99, 55U35
Keywords: model category, locally presentable category, poset, small category, Alexandroff space, classifying space 
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     pages = {211--230},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2010.v12.n2.a7/}
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George Raptis. Homotopy theory of posets. Homology, homotopy, and applications, Tome 12 (2010) no. 2, pp. 211-230. doi : 10.4310/HHA.2010.v12.n2.a7. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2010.v12.n2.a7/

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