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    • CommentRowNumber1.
    • CommentAuthorDavidRoberts
    • CommentTimeDec 2nd 2010

    Apologies for the slew of paper related questions, but this one was bugging me too.

    Given a pretopology, or more generally, a coverage JJ on a category, and the class of arrows (JJ-epi) of arrows that admit local sections relative to JJ. This class is interesting, but I’m interested in the subclass of arrows of which all pullbacks exist and which is stable under pullback (hence forms another pretopology). I denoted this J singJ_{sing} in my paper, because it is, if you like, the singletonification of JJ. This is clearly a Bad Name (TM), but I can’t think of a good name. ’The class of pullback-stable JJ-epimorphisms’ is also too much of a mouthful. It’s a sort of saturation of JJ, but isn’t saturated as I define the notion (and I have good reason to keep the definition of saturation as is).

    Any ideas?

    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeDec 2nd 2010

    “universally J-epic”? (To go along with “universally effective-epimorphic.”)

    • CommentRowNumber3.
    • CommentAuthorDavidRoberts
    • CommentTimeDec 2nd 2010

    let me try it:

    “Let J uJ_u be the class of universally JJ-epi maps.”

    (where now J singJ uJ_{sing} \mapsto J_u) Hmm. Then there is a nice double meaning to the u{}_u, as it is an abbreviation of un. How about J unJ_{un}? Is it too much of a pun?

    • CommentRowNumber4.
    • CommentAuthorTobyBartels
    • CommentTimeDec 3rd 2010

    What’s the pun? Is it French? (I still don’t see the pun.)

    By the way, I have seen “arrows of which all pullbacks exist” called “carrable”, which seems to be the same French word showing up on this nLab page (although not with quite the same meaning).

    • CommentRowNumber5.
    • CommentAuthorDavidRoberts
    • CommentTimeDec 4th 2010

    unun as in universal, and also as a singleton pretopology (of course, un = one). I’ll go with J unJ_{un} I think.

    • CommentRowNumber6.
    • CommentAuthorTobyBartels
    • CommentTimeDec 4th 2010

    Yes, of course, I forgot the meaning behind the original symbol!

    I also like the Anglo-French pun 𝔽 un\mathbb{F}_{un}.