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1. • CommentRowNumber1.
   • CommentAuthorDavid_Corfield
   • CommentTimeDec 10th 2012
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   Author: David_Corfield
   Format: MarkdownItexIf "All concepts are Kan extensions," "The notion of Kan extensions subsumes all the other fundamental concepts of category theory," etc., shouldn't we expect categorical logic to have something to say about them? And, in particular, won't homotopy type theory have something to say about [[(infinity,1)-Kan extensions]]?

   If “All concepts are Kan extensions,” “The notion of Kan extensions subsumes all the other fundamental concepts of category theory,” etc., shouldn’t we expect categorical logic to have something to say about them? And, in particular, won’t homotopy type theory have something to say about (infinity,1)-Kan extensions?

2. • CommentRowNumber2.
   • CommentAuthorDavid_Corfield
   • CommentTimeDec 10th 2012
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   Author: David_Corfield
   Format: MarkdownItexHmm, maybe if it is logical in some sense, then it's [2-logical](http://www.ncatlab.org/michaelshulman/show/2-categorical+logic).

   Hmm, maybe if it is logical in some sense, then it’s 2-logical.

3. • CommentRowNumber3.
   • CommentAuthorMike Shulman
   • CommentTimeDec 10th 2012
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   Author: Mike Shulman
   Format: MarkdownItexYeah, that was about to be my reply. (-:

   Yeah, that was about to be my reply. (-:

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeDec 10th 2012
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   Author: Urs
   Format: MarkdownItexOf couse there is Kan extension in dependent sum/product.

   Of couse there is Kan extension in dependent sum/product.