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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] also as an Example at monoidal topos. And I guess we should still add a pointer to an explanation of 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(FinSetop) is the classifying topos for objects by pointing to this fact.

    (Just for completeness.)

    Also added the remark that similarly PSh((FinSet*)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 -case:


    Similarly

    • PSh(FinSetop*) is the classifying topos for pointed objects.

    • write FinGrpd for the full sub-(∞,1)-category on ∞Grpd which is generated under finite (∞,1)-colimits from the point * (HA, def. 1.4.2.8), then the (∞,1)-presheaf (∞,1)-topos PSh(FinGrpdop) is the classifying (∞,1)-topos for objects;

    • write FinGrpd* for pointed finite -groupoids in this sense, then PSh((FinGrpd*)op) is the classifying (,1)-topos for pointed objects. See also at spectrum object via excisive functors.

    • 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].

    diff, v24, current