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nLab > Latest Changes: closed bicategory

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  1.  
    • CommentRowNumber1.
    • CommentAuthorMike Shulman
    • CommentTimeJul 7th 2021

    Created stub.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorvarkor
    • CommentTimeJul 7th 2021

    Added a definition.

    diff, v2, current

    • CommentRowNumber3.
    • CommentAuthorvarkor
    • CommentTimeJul 7th 2021

    Mention coclosed bicategories.

    diff, v2, current

    • CommentRowNumber4.
    • CommentAuthorMike Shulman
    • CommentTimeJul 8th 2021

    What I wrote was already a definition!

    I’ve never heard this terminology “coclosed bicategory”, do you have a reference? I’m wary particularly of “biclosed bicategory” because I think I’ve heard that used to mean what here we’ve called just a “closed bicategory” (i.e. admitting both right extensions and right lifts, either one being a sort of “left closed” or “right closed”).

    • CommentRowNumber5.
    • CommentAuthorvarkor
    • CommentTimeJul 8th 2021

    What I wrote was already a definition!

    I didn’t say that there wasn’t already a definition, just that I added (a new) one ;) I’ve tweaked the introduction to make it clearer those are two equivalent definitions.

    I’ve never heard this terminology “coclosed bicategory”, do you have a reference?

    I’ve seen it used in a few places, e.g. An extended view of the Chu-construction, Morphisms and modules for poly-bicategories, Weak units, universal cells, and coherence via universality for bicategories. It’s also the natural naming convention.

    I agree “biclosed bicategory” is less clear, and I have also seen it to mean “closed” in the sense of the nLab page. However, I do think it’s a sensible naming convention. Do you have any alternative suggestions? Perhaps it’s an uncommon enough concept that it’s not necessary to give a name.

    • CommentRowNumber6.
    • CommentAuthorMike Shulman
    • CommentTimeJul 9th 2021

    I’d probably say “closed and co-closed” if I had to.

    • CommentRowNumber7.
    • CommentAuthorBryceClarke
    • CommentTimeJul 11th 2021
    • (edited Jul 11th 2021)

    Added example to Span(E)Span(E) being a closed bicategory and the earliest reference of this fact that I could find:

    diff, v4, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeMay 26th 2022

    added pointer to:

    • Renato Betti, Robert F. C. Walters, Closed bicategories and variable category theory, Universita degli Studi di Milano (1985), reprinted in: Reprints in Theory and Applications of Categories, 26 (2020) 1-27 [[tac:tr26]]

    diff, v5, current

1 to 8 of 8

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