[AaronFriel]

Self duals are entirely reasonable! A unified theory of food would be incomplete if we excluded such beautiful symmetries.

[andybak]

So where are we heading?

It seems we might slip from group theory to category theory. At which point we are surely describing the structure of meta-sandwiches (in that they sandwich various definitions of sandwichness between each other)

[AaronFriel]

I think you're onto something, after all burritos are just endofunctors in the category of monoids.