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    • CommentRowNumber1.
    • CommentAuthorFinnLawler
    • CommentTimeNov 26th 2010

    New page: bicategory of maps.

    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeNov 27th 2010

    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?

    • CommentRowNumber3.
    • CommentAuthorFinnLawler
    • CommentTimeNov 27th 2010

    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 KMK \to M, the equipment MapMMMap M \to M is its ’objectwise Cauchy completion’?

    • CommentRowNumber4.
    • CommentAuthorMike Shulman
    • CommentTimeNov 28th 2010

    Yes, I think it might make sense to view the construction of MapMMMap M \to M from KMK\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.

    • CommentRowNumber5.
    • CommentAuthorFinnLawler
    • CommentTimeDec 1st 2010

    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.