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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeMay 11th 2010
    • (edited May 11th 2010)
    • CommentRowNumber2.
    • CommentAuthorEric
    • CommentTimeMay 11th 2010

    FYI: If you have a typo in the subject of a post, you can change it by editing the original comment.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeMay 11th 2010

    Thanks, Eric! I didn’t know that, but did wonder about it. Good, so I fixed the typo.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeMay 11th 2010

    I am now pretty much through with completing and polishing that section on Spaces of infinitesimal simplices.

    I feel this improves considerably in its detail and exposition style over stuff I had previously typed at infinitesimal singular simplicial complex and eventually I will try to go through that entry and polish it accordingly.

    For the moment though I would just want to advertize: not that i think this is anything close to perfect, but in case anyone ever wondered where the heck actually the magic occurs in Anders Kock’s discussion of combinatorial differential forms in a smooth topos: the crucial argument is a very elementary and simple one, which needs neither the (internal) topos (logic) perspective nor in fact the comparatively complicated (it seems) formulas from Breen-Messing’s article, but is really just a simple statement about certain very simple finitely-presented commutative cosimplicial \mathbb{R}-algebras. This I try to expose at Spaces of infinitesimal simplices. I am not claiming that my exposition is not in need of more improvement, but it seems to me that this is a useful clarification (and if only a more focused highlighting) of some things one may find in some literature.

  1. It was stated below definition 2.1 that an internally small object is an externally small object (the corresponding nLab page about tiny objects was linked). I believe that this is incorrect, so I edited the paragraph accordingly.

    Nico Beck

    diff, v48, current