HOMOTOPY THEORY OF POSETS

Autor(en): Raptis, George
Stichwörter: Alexandroff space; classifying space; FINITE TOPOLOGICAL SPACES; locally presentable category; Mathematics; Mathematics, Applied; MODEL CATEGORIES; model category; poset; small category
Erscheinungsdatum: 2010
Herausgeber: INT PRESS BOSTON, INC
Journal: HOMOLOGY HOMOTOPY AND APPLICATIONS
Volumen: 12
Ausgabe: 2
Startseite: 211
Seitenende: 230
Zusammenfassung: 
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.
ISSN: 15320073
DOI: 10.4310/HHA.2010.v12.n2.a7

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