Volume 10, issue 1 (2010)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Faithfulness of a functor of Quillen

William G Dwyer, Andrei Rădulescu-Banu and Sebastian Thomas

Algebraic & Geometric Topology 10 (2010) 525–530
Abstract

There exists a canonical functor from the category of fibrant objects of a model category modulo cylinder homotopy to its homotopy category. We show that this functor is faithful under certain conditions, but not in general.

Keywords
model categories, fibrant objects, cofibrant objects, homotopy, faithful
Mathematical Subject Classification 2000
Primary: 18G55, 55U35
References
Publication
Received: 6 October 2009
Accepted: 4 December 2009
Published: 7 March 2010
Authors
William G Dwyer
Department of Mathematics
University of Notre Dame
Notre Dame, IN 46556
USA
http://www.nd.edu/~wgd/
Andrei Rădulescu-Banu
86 Cedar St
Lexington, MA 02421
USA
Sebastian Thomas
Lehrstuhl D für Mathematik
RWTH Aachen University
Templergraben 64
D-52062 Aachen
Germany
http://www.math.rwth-aachen.de/~Sebastian.Thomas/