A Small Observation

July 3, 2008

Posted by David Corfield

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Urs defined the Schreiber 2-group of linear automorphisms of a skeletal Baez-Crans 2-vector space back here. For the space $δ = 0 : F^{n} \to F^{m}$ , it has $GL (n, F) \times GL (m, F)$ as objects and $F^{n \cdot m}$ worth of arrows from an object to itself. Arrows are linear maps $F^{n} \to F^{m}$ , and the group of objects acts on them by a kind of composition.

Now, the small thought occurred to me that interchanging the $m$ and $n$ makes little difference. So when I suggested that the Poincaré 2-group was a sub-2-group of the 2-group for $n = 1, m = 4$ , I might also have said $n = 4, m = 1$ .

But all this is not so surprising, as this area is quite span-ish and bimodule-esque.

Posted at July 3, 2008 4:35 PM UTC

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July 3, 2008