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1. • CommentRowNumber1.
   • CommentAuthorHarry Gindi
   • CommentTimeJul 30th 2010
   • (edited Jul 30th 2010)
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   Author: Harry Gindi
   Format: MarkdownItexHow do we show that in a model category, the left derived functor defined as the right Kan extension along the localization functor $C\to Ho(C)$ of the composite $C\to D\to Ho(D)$ agrees with the definition using fibrant/cofibrant replacements? If it's in DHKS, could you give the chapter number?

   How do we show that in a model category, the left derived functor defined as the right Kan extension along the localization functor $C\to Ho(C)$ of the composite $C\to D\to Ho(D)$ agrees with the definition using fibrant/cofibrant replacements?

   If it’s in DHKS, could you give the chapter number?

2. • CommentRowNumber2.
   • CommentAuthorMike Shulman
   • CommentTimeJul 30th 2010
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   Author: Mike Shulman
   Format: MarkdownItexI don't remember exactly where it is off the top of my head. Have you tried to prove it yourself? My recollection is that it's a pretty easy exercise, using the fact that functors out of Ho(C) are the same as weak-equivalence-inverting functors out of C.

   I don’t remember exactly where it is off the top of my head. Have you tried to prove it yourself? My recollection is that it’s a pretty easy exercise, using the fact that functors out of Ho(C) are the same as weak-equivalence-inverting functors out of C.