Homology, Homotopy and Applications
- Homology Homotopy Appl.
- Volume 12, Number 2 (2010), 211-230.
Homotopy theory of posets
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.
Homology Homotopy Appl. Volume 12, Number 2 (2010), 211-230.
First available in Project Euclid: 28 January 2011
Permanent link to this document
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
Raptis, George. Homotopy theory of posets. Homology Homotopy Appl. 12 (2010), no. 2, 211--230. https://projecteuclid.org/euclid.hha/1296223882.