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1. • CommentRowNumber1.
   • CommentAuthorHarry Gindi
   • CommentTimeJun 6th 2010
   • (edited Jun 6th 2010)
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   Author: Harry Gindi
   Format: MarkdownItexI moved the characterization of pointwise [[kan extension|kan extensions]] as those preserved by representable functors to the top (of the section on pointwise kan extensions) and made it the definition (since there was no unified definition before). This is for aesthetic reasons. Since being pointwise is a _property_, I like that this property has a definition independent of the computational model we're using. Are there size issues that I might be glossing over?

   I moved the characterization of pointwise kan extensions as those preserved by representable functors to the top (of the section on pointwise kan extensions) and made it the definition (since there was no unified definition before). This is for aesthetic reasons. Since being pointwise is a property, I like that this property has a definition independent of the computational model we’re using.

   Are there size issues that I might be glossing over?

2. • CommentRowNumber2.
   • CommentAuthorMike Shulman
   • CommentTimeJun 6th 2010
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   Author: Mike Shulman
   Format: MarkdownItexWell, "representable functors" only exist if your category is locally small, or if you use a higher universe in which for them to take values, if that's what you're thinking of. I don't think we need to dwell on anything like that at [[Kan extension]] though.

   Well, “representable functors” only exist if your category is locally small, or if you use a higher universe in which for them to take values, if that’s what you’re thinking of. I don’t think we need to dwell on anything like that at Kan extension though.