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    • CommentRowNumber1.
    • CommentAuthorMike Shulman
    • CommentTimeApr 6th 2010

    Added some comments about the possibility of 2-dimensional unbiased composites in double categories.

    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeApr 7th 2010

    Created tileorder with the two characterizations due to Dawson-Pare.

    • CommentRowNumber3.
    • CommentAuthorTodd_Trimble
    • CommentTimeApr 7th 2010

    I've put a query under the definition section of tileorder.

    • CommentRowNumber4.
    • CommentAuthorMike Shulman
    • CommentTimeApr 8th 2010

    I replied. If this answers your question, feel free to remove the query box and clarify the entry so that other people don’t have the same question.

    • CommentRowNumber5.
    • CommentAuthorTodd_Trimble
    • CommentTimeApr 8th 2010

    Thanks Mike -- it did answer the question (and I should have read what you wrote more carefully). Probably it's not necessary to change anything, but I'll take another look in a moment.

    • CommentRowNumber6.
    • CommentAuthorEric
    • CommentTimeApr 8th 2010
    • (edited Apr 8th 2010)

    Interesting. I started typing out a question the other day, but don’t remember if I posted it, along the lines, “Is there a term for the analogue of preorder in a double category?” I guess this term would be tileorder?

    I think you are overlapping with my dream of nPOV’ing (I like using nPOV as a verb these days) our discrete geometry stuff on directed n-cubes (or n-diamonds). The stuff on tileorder makes me think of a 2-diamond complex.

    Oh I wish I was smarter…

    Edit: I feel like my brain is going to explode. Urs and Domenico are blowing my mind. Mike and Todd are both doing stuff that is getting close to my heart. I’ve said it before, but I often feel like Salieri’s character in Amadeus. I know just enough to appreciate the beauty of what you guys are doing, but tortured by not having the ability to create it myself.