Geodesic
Faithfulness of a functor of Quillen
Dwyer, William G1 ; Rădulescu-Banu, Andrei2 ; Thomas, Sebastian3
1Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556, USA
286 Cedar St, Lexington, MA 02421, USA
3Lehrstuhl D für Mathematik, RWTH Aachen University, Templergraben 64, D-52062 Aachen, Germany
Algebraic and Geometric Topology, Tome 10 (2010) no. 1, pp. 525-530
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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.

DOI : 10.2140/agt.2010.10.525
Keywords: model categories, fibrant objects, cofibrant objects, homotopy, faithful

Dwyer, William G  1   ; Rădulescu-Banu, Andrei  2   ; Thomas, Sebastian  3

1 Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556, USA
2 86 Cedar St, Lexington, MA 02421, USA
3 Lehrstuhl D für Mathematik, RWTH Aachen University, Templergraben 64, D-52062 Aachen, Germany 
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Dwyer, William G; Rădulescu-Banu, Andrei; Thomas, Sebastian. Faithfulness of a functor of Quillen. Algebraic and Geometric Topology, Tome 10 (2010) no. 1, pp. 525-530. doi: 10.2140/agt.2010.10.525

[1] K S Brown, Abstract homotopy theory and generalized sheaf cohomology, Trans. Amer. Math. Soc. 186 (1974) 419

[2] D Happel, Triangulated categories in the representation theory of finite-dimensional algebras, London Math. Society Lecture Note Ser. 119, Cambridge Univ. Press (1988)

[3] P S Hirschhorn, Model categories and their localizations, Math. Surveys and Monogr. 99, Amer. Math. Soc. (2003)

[4] M Hovey, Model categories, Math. Surveys and Monogr. 63, Amer. Math. Soc. (1999)

[5] D G Quillen, Homotopical algebra, Lecture Notes in Math. 43, Springer (1967)

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