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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeFeb 2nd 2011
    • (edited Feb 2nd 2011)

    I notice that the entry essential image is in a bad state:

    it starts out making two statements, the first of which is then doubted by Mike in a query box, the second doubted by Zoran in a query box.

    If there is really no agreement on what should go there, we should maybe better clear the entry, and discuss the matter here until we have a minimum of consensus.

    But I guess the problems can easily be dealt with and somebody should try to polish this entry right away.

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeFeb 2nd 2011

    As far as my complaint, Toby answered to it, my memory is that I was happy with his remark at the time. So, if he puts it his way with the subtlety discussed I am happy with move of the second box to here after that (with backlink). As far as Mike’s comment, I was at the time pretty sure that the definition worked very well in the world of strict n-categories at least and did not quite understand the pseudomonicity complaint. That part is not resolved as far as I am concerned.

    • CommentRowNumber3.
    • CommentAuthorMike Shulman
    • CommentTimeFeb 4th 2011

    You are right, I think; pseudomonicity is only required if you want the essential image to be equivalent to the strict image. I’ve updated replete subcategory and essential image along these lines. I’m curious, though, whether there is any use for non-full essential images as defined on that page?

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeFeb 4th 2011

    Thanks for taking the time to brush up that entry!