Faithfulness of a functor of Quillen
William G. Dwyer, Andrei Rădulescu-Banu, Sebastian Thomas
Algebraic & Geometric Topology 10(1) (2010), pp. 525-530.
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.
fulltext, arXiv:0910.1038, journal, DOI: 10.2140/agt.2010.10.525, MR2737327, Zbl 1218.18011
