MODEL CATEGORIES (Mathematical Surveys and Monographs 63)

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Rational homotopy theory: a brief introduction (2006, background): “The author would like to thank Chris Allday, Luchezar Avramov, Srikanth Iyengar, Mike Mandell and Jonathan Scott, as well as the anonymous referee, for their helpful comments on an earlier version of this article.”
Real homotopy theory of semi-algebraic sets (2008, background): “In that proof, functors such as C∗(−) and ΩPA(−) need to be extended from objects to operads, but this can only be done if these functors are symmetric monoidal (a basic reference for symmetric monoidal categories is [15]).”
On the homotopy theory of enriched categories (2012, background): “The theory of Quillen model categories [10, 11, 17] provides a powerful framework to treat these examples in a systematic way.”
Long knots and maps between operads (2010, background): “In this section we develop basic properties of model categories which we will need later on; [12] and [7] are two background references.”