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1. • CommentRowNumber1.
   • CommentAuthorDavid_Corfield
   • CommentTimeNov 20th 2012
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexIf [[equivalence]] is treated so generally, couldn't [[natural equivalence]] too, or is its restriction to 2-categories of 2-functors been determined by use? But then what is the general notion of 'naturalness' as applied to equivalences in general to be called? And how is it defined? This relates to a [question](http://golem.ph.utexas.edu/category/2012/11/freedom_from_logic.html#c042550) I posed to Mike. While I'm on this subject, >The general theory of equivalence is discussed at [[equivalence relation]]... Is it? It seems to be a rather limited notion of equivalence discussed there.

   If equivalence is treated so generally, couldn’t natural equivalence too, or is its restriction to 2-categories of 2-functors been determined by use? But then what is the general notion of ’naturalness’ as applied to equivalences in general to be called? And how is it defined? This relates to a question I posed to Mike.

   While I’m on this subject,

   The general theory of equivalence is discussed at equivalence relation…

   Is it? It seems to be a rather limited notion of equivalence discussed there.

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeNov 20th 2012
   • (edited Nov 20th 2012)
   • PermaLink
   Author: Urs
   Format: MarkdownItexHm, but a natural equivalence is just an equivalence between functors. Need not be 1-functors or 2-functors. Could be $\infty$-functors.

   Hm, but a natural equivalence is just an equivalence between functors. Need not be 1-functors or 2-functors. Could be $\infty$-functors.

3. • CommentRowNumber3.
   • CommentAuthorTobyBartels
   • CommentTimeNov 20th 2012
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   Author: TobyBartels
   Format: MarkdownItexI changed the ‘general theory’ sentence at [[equivalence]].

   I changed the ‘general theory’ sentence at equivalence.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeNov 20th 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have edited the text at _[[natural equivalence]]_ a little more.

   I have edited the text at natural equivalence a little more.

5. • CommentRowNumber5.
   • CommentAuthorMike Shulman
   • CommentTimeNov 20th 2012
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   Author: Mike Shulman
   Format: MarkdownItexArguably, "natural equivalence" is just the particular case of equivalence where the objects you're talking about are functors.

   Arguably, “natural equivalence” is just the particular case of equivalence where the objects you’re talking about are functors.