Homology, Homotopy and Applications

Homotopy theory of posets

George Raptis

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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 → 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 T0-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.

Article information

Homology Homotopy Appl. Volume 12, Number 2 (2010), 211-230.

First available in Project Euclid: 28 January 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 18G55: Homotopical algebra 18B35: Preorders, orders and lattices (viewed as categories) [See also 06-XX] 55U35: Abstract and axiomatic homotopy theory 54G99: None of the above, but in this section

Model category locally presentable category poset small category Alexandroff space classifying space


Raptis, George. Homotopy theory of posets. Homology Homotopy Appl. 12 (2010), no. 2, 211--230. http://projecteuclid.org/euclid.hha/1296223882.

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