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1. • CommentRowNumber1.
   • CommentAuthorFinnLawler
   • CommentTimeNov 26th 2010
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   Author: FinnLawler
   Format: MarkdownItexNew page: [[bicategory of maps]].

   New page: bicategory of maps.

2. • CommentRowNumber2.
   • CommentAuthorMike Shulman
   • CommentTimeNov 27th 2010
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   Author: Mike Shulman
   Format: MarkdownItexNice, thank you. I added a bit. Are you going to also include the characterization of bicategories of spans, since you added a link to that paper?

   Nice, thank you. I added a bit. Are you going to also include the characterization of bicategories of spans, since you added a link to that paper?

3. • CommentRowNumber3.
   • CommentAuthorFinnLawler
   • CommentTimeNov 27th 2010
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   Author: FinnLawler
   Format: MarkdownItexThanks for the additions (and the redirects!). I've added an extra sentence summarizing Lack--Walters--Wood's main result, but there's a lot more to say. I should get around to expanding it next week (though that's not meant to discourage anyone else from doing it!). The bit about the universal equipment on a bicategory is interesting. Would it make sense to say that, for an equipment $K \to M$, the equipment $Map M \to M$ is its 'objectwise Cauchy completion'?

   Thanks for the additions (and the redirects!). I’ve added an extra sentence summarizing Lack–Walters–Wood’s main result, but there’s a lot more to say. I should get around to expanding it next week (though that’s not meant to discourage anyone else from doing it!).

   The bit about the universal equipment on a bicategory is interesting. Would it make sense to say that, for an equipment $K \to M$, the equipment $Map M \to M$ is its ’objectwise Cauchy completion’?

4. • CommentRowNumber4.
   • CommentAuthorMike Shulman
   • CommentTimeNov 28th 2010
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   Author: Mike Shulman
   Format: MarkdownItexYes, I think it might make sense to view the construction of $Map M \to M$ from $K\to M$ as first "adjoining Cauchy completions for all objects," then restricting to the subcategory of Cauchy complete objects. However, I don't know exactly what the first operation would mean all by itself.

   Yes, I think it might make sense to view the construction of $Map M \to M$ from $K\to M$ as first “adjoining Cauchy completions for all objects,” then restricting to the subcategory of Cauchy complete objects. However, I don’t know exactly what the first operation would mean all by itself.

5. • CommentRowNumber5.
   • CommentAuthorFinnLawler
   • CommentTimeDec 1st 2010
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   Author: FinnLawler
   Format: MarkdownItexI've added another sentence about Lack et. al.'s result (yes, I work slowly). There's more to be said about Frobenius and separable objects, and about comonads and their relationship to idempotents in allegories, but that'll take some more figuring out, and might fit better on other pages.

   I’ve added another sentence about Lack et. al.’s result (yes, I work slowly). There’s more to be said about Frobenius and separable objects, and about comonads and their relationship to idempotents in allegories, but that’ll take some more figuring out, and might fit better on other pages.