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