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nLab > Latest Changes: representable 2-category

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  1.  
    • CommentRowNumber1.
    • CommentAuthorvarkor
    • CommentTimeSep 26th 2021

    Create a stub page.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorvarkor
    • CommentTimeSep 26th 2021

    I apologise in advance for the format of the page and the citation style. Is there a way we can generate the appropriate citations directly from BibTeX? It is tedious to do so by hand.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeSep 26th 2021

    here is what I do, it’s easy:

    • send Google the paper title

    • find the published page among the first few hits

    • click on “cite as” or similar

    • copy-and-paste what it offers:

    In the present case I immediately get this:

    • John Gray, The meeting of the Midwest Category Seminar in Zurich August 24–30, 1970, Lecture Notes in Mathematics, vol 195. Springer 1971, pp. 254–255 (doi:10.1007%2FBFb0072315)

    diff, v2, current

    • CommentRowNumber4.
    • CommentAuthorvarkor
    • CommentTimeSep 26th 2021

    Ah, I see, thank you!

    • CommentRowNumber5.
    • CommentAuthorzskoda
    • CommentTimeSep 4th 2024

    Can you comment on what is the raison behind the terminology ?

  6. I haven’t checked the references, but am pretty sure it refers to recovering a 2-category as the 2-category Hom(A op,CAT)\mathsf{Hom}(A^{op}, \mathsf{CAT}) for some AA. In other words, one can glue various 2-categories together to recover one’s original one. This is where the interval category in the conditions comes in: it is pretty obvious that one can build up any category by gluing together intervals and imposing equality conditions on arrows, and this is just an enrichment of that idea.

    Gluing

    diff, v4, current

    • CommentRowNumber7.
    • CommentAuthorAlexanderCampbell
    • CommentTimeSep 4th 2024
    • (edited Sep 4th 2024)
    My recollection is that such a 2-category was called representable simply because certain limit constructions are representable in it. I don't remember now whether I got that from Gray's (or Street's) writing or from my own imagination. I would regard this as obsolete terminology.

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