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1. • CommentRowNumber1.
   • CommentAuthorMike Shulman
   • CommentTimeDec 29th 2009
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   Author: Mike Shulman
   Format: MarkdownA lot of people seem to think that the word "model" in the term "model category" refers to the *category* as a "model for a homotopy theory." However, on page 0.3 of Quillen's "Homotopical Algebra" we find: > The term "model category" is short for "a category of models for a homotopy theory." In other words, it is the *objects* of the model category which are models. (This is a [noun adjunct](http://en.wikipedia.org/wiki/Noun_adjunct), which is perfectly normal English usage.) Now of course it's also true, and a helpful way to think, that the model category itself is a model for an (?,1)-category, but I don't think that's what Quillen intended "model" to mean.

   A lot of people seem to think that the word "model" in the term "model category" refers to the category as a "model for a homotopy theory." However, on page 0.3 of Quillen's "Homotopical Algebra" we find:

   The term "model category" is short for "a category of models for a homotopy theory."

   In other words, it is the objects of the model category which are models. (This is a noun adjunct, which is perfectly normal English usage.) Now of course it's also true, and a helpful way to think, that the model category itself is a model for an (?,1)-category, but I don't think that's what Quillen intended "model" to mean.

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeDec 29th 2009
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   Author: Urs
   Format: MarkdownThanks, Mike. I should have looked it up myself. Thanks.

   Thanks, Mike. I should have looked it up myself. Thanks.

3. • CommentRowNumber3.
   • CommentAuthorzskoda
   • CommentTimeDec 29th 2009
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   Author: zskoda
   Format: MarkdownI agree with Mike upon reading some other works from 1970-s which follow Quillen and where there was no doubt that the objects are models.

   I agree with Mike upon reading some other works from 1970-s which follow Quillen and where there was no doubt that the objects are models.