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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeAug 8th 2013

    I have splitt off from classifying topos an entry classifying topos for the theory of objects and added the statement about the relation to finitary monads.

    • CommentRowNumber2.
    • CommentAuthorTodd_Trimble
    • CommentTimeAug 8th 2013

    I added to your remark a related point of view, and linked to some notes of mine.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeAug 8th 2013
    • (edited Aug 8th 2013)

    Ah, thanks, that’s nice!!

    We should add some kind of remark concerning [ op,Set][\mathbb{P}^{op}, Set] also as an Example at monoidal topos. And I guess we should still add a pointer to an explanation of \mathbb{P} to the entry. I can’t right now, though, am in a rush here…

    • CommentRowNumber4.
    • CommentAuthorMike Shulman
    • CommentTimeAug 8th 2013

    Nice page, thanks.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeAug 9th 2013

    I have added a stub for permutation category, just for completeness. In the course of this I noticed that we already have braid category! I have now cross-linked that a bit more such as to make it easier to find.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeNov 26th 2014
    • (edited Nov 26th 2014)

    Spelled out here the argument for why PSh(FinSet op)PSh(FinSet^{op}) is the classifying topos for objects by pointing to this fact.

    (Just for completeness.)

    Also added the remark that similarly PSh((FinSet *) op)PSh((FinSet_\ast)^{op}) is the classifying topos for pointed objects.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeNov 26th 2014

    added also at classifying topos for the theory of objects remarks on the \infty-case:


    Similarly

    • Added remarks on “finite” in FinSet.
    • Added remarks on object classifier as generalized space of “sets”

    Steve Vickers

    diff, v21, current

  1. Added more concrete construction of the pointed set classifier.

    Steve Vickers

    diff, v21, current

    • CommentRowNumber10.
    • CommentAuthorThomas Holder
    • CommentTimeNov 27th 2018

    Fixed some typos and highlighted (hopefully in a correct way) the role of the category of elements in this. It would be nice if one could bring the description of the generic object in section 2 notationally and conceptually in line with the description given in the current section 3 ! Thanks anyway for polishing the entries on ’geometric’ logics and adding clarifications !

    diff, v22, current

    • CommentRowNumber11.
    • CommentAuthorDavidRoberts
    • CommentTimeNov 27th 2018

    Linked to the page finite set in the comments about what finite sets are meant for [FinSet,Set][FinSet, Set].

    diff, v24, current

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