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1. • CommentRowNumber1.
   • CommentAuthorHarry Gindi
   • CommentTimeSep 15th 2010
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   Author: Harry Gindi
   Format: MarkdownItexFollowing sections 34 and 35 in Dwyer-Hirschhorn-Kan-Smith (DHKS), I have begun to write up a page on hammock localization and simplicial Grothendieck construction localization. [[simplicial localization of a homotopical category]].

   Following sections 34 and 35 in Dwyer-Hirschhorn-Kan-Smith (DHKS), I have begun to write up a page on hammock localization and simplicial Grothendieck construction localization. simplicial localization of a homotopical category.

2. • CommentRowNumber2.
   • CommentAuthorHarry Gindi
   • CommentTimeSep 15th 2010
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   Author: Harry Gindi
   Format: MarkdownItexI should also add that I'm a bit unhappy with the way that DHKS define the morphisms induced by maps in $\mathbf{T}$. For some reason, the functors they want us to use, $f_*$ don't seem like they're the "right" ones categorically. It seems much more natural for us to use the pullback $f^*$, since that is just precomposition, but for some reason, the maps $f_*$ are used instead. Are they at least adjoint to the $f^*$, or are they as arbitrary as they seem?

   I should also add that I’m a bit unhappy with the way that DHKS define the morphisms induced by maps in $\mathbf{T}$. For some reason, the functors they want us to use, $f_*$ don’t seem like they’re the “right” ones categorically. It seems much more natural for us to use the pullback $f^*$, since that is just precomposition, but for some reason, the maps $f_*$ are used instead. Are they at least adjoint to the $f^*$, or are they as arbitrary as they seem?

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeSep 16th 2010
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   Author: Urs
   Format: MarkdownItexHi Harry, that's great that you are doing this, thanks! Eventually it would be good if you added hyperlinks back and forth between the entry you are writing and the relavant existing nLab entries. I'd actually tend to think it deserves to be merged with [[simplicial localization]].

   Hi Harry,

   that’s great that you are doing this, thanks!

   Eventually it would be good if you added hyperlinks back and forth between the entry you are writing and the relavant existing nLab entries. I’d actually tend to think it deserves to be merged with simplicial localization.

4. • CommentRowNumber4.
   • CommentAuthorHarry Gindi
   • CommentTimeSep 16th 2010
   • (edited Sep 16th 2010)
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   Author: Harry Gindi
   Format: MarkdownItex@Urs: Thanks! It's nice to feel appreciated =)! Also, the induced functors $f_*$ impose the relations that we want for localization, but I'd still like to know why that's a natural choice (is it actually adjoint to the pullback?) if anyone could tell me that.

   @Urs: Thanks! It’s nice to feel appreciated =)!

   Also, the induced functors $f_*$ impose the relations that we want for localization, but I’d still like to know why that’s a natural choice (is it actually adjoint to the pullback?) if anyone could tell me that.