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    • CommentRowNumber1.
    • CommentAuthorSridharRamesh
    • CommentTimeDec 11th 2019
    • (edited Dec 11th 2019)

    In double category#Unbiased, it is noted “(It is tempting to try to axiomatize such a structure finitely by adding a basic “pinwheel-composition” operation, but although every non-composable arrangement reduces to one “containing” a pinwheel, the containment is not necessarily of a sort to which such an operation could be applied. So it is not clear whether there is any finitary axiomatization of such “augmented” double categories.)”.

    Is it easy to provide an example illustration of a rectangular configuration of smaller rectangles which could not be composed even after the addition of a “pinwheel-composition” operation to those of a double category?

    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeDec 12th 2019

    Good question! I didn’t remember offhand, but after looking back at some of my notes on this subject from a few years ago, I found one and added it to the page.

    • CommentRowNumber3.
    • CommentAuthorSridharRamesh
    • CommentTimeDec 13th 2019

    Ah, perfect. This example clears things up very nicely. Thanks!