Faithfulness of a functor of Quillen

Dwyer, William G; Rădulescu-Banu, Andrei; Thomas, Sebastian

doi:10.2140/agt.2010.10.525

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Faithfulness of a functor of Quillen

William G Dwyer, Andrei Rădulescu-Banu and Sebastian Thomas

Algebraic & Geometric Topology 10 (2010) 525–530

DOI: 10.2140/agt.2010.10.525

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/

Volume 10, issue 1 (2010)