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1. • CommentRowNumber1.
   • CommentAuthorHarry Gindi
   • CommentTimeJul 4th 2010
   • PermaLink
   Author: Harry Gindi
   Format: MarkdownItexIn the proof of proposition 2.2.3.4 of HTT, Lurie says we can give a lift by looking at maps $A\times S\coprod_{A\times S'} B\times S'\subseteq B\times S$ for any right anodyne map $A\to B$. Now, I understand why that works if we replace the $S$ and $S'$ in the display with $X$ and $X'$ respectively, but it doesn't make sense to me otherwise. Would someone mind checking and confirming whether or not it's a typo? If it's not a typo, could you explain why we can reduce the lifting problem for $A\times X\coprod_{A\times X'} B\times X'\subseteq B\times X$ to the map $A\times S\coprod_{A\times S'} B\times S'\subseteq B\times S$? Thanks.

   In the proof of proposition 2.2.3.4 of HTT, Lurie says we can give a lift by looking at maps $A\times S\coprod_{A\times S'} B\times S'\subseteq B\times S$ for any right anodyne map $A\to B$. Now, I understand why that works if we replace the $S$ and $S'$ in the display with $X$ and $X'$ respectively, but it doesn’t make sense to me otherwise.

   Would someone mind checking and confirming whether or not it’s a typo? If it’s not a typo, could you explain why we can reduce the lifting problem for $A\times X\coprod_{A\times X'} B\times X'\subseteq B\times X$ to the map $A\times S\coprod_{A\times S'} B\times S'\subseteq B\times S$?

   Thanks.

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeJul 5th 2010
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   Author: Urs
   Format: MarkdownItexYes. Typo, exactly as you say.

   Yes. Typo, exactly as you say.

3. • CommentRowNumber3.
   • CommentAuthorHarry Gindi
   • CommentTimeJul 5th 2010
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   Author: Harry Gindi
   Format: MarkdownItexThanks a lot!

   Thanks a lot!