## July 3, 2008

### A Small Observation

#### Posted by David Corfield

Urs defined the Schreiber 2-group of linear automorphisms of a skeletal Baez-Crans 2-vector space back here. For the space $\delta =0:{F}^{n}\to {F}^{m}$, it has $\mathrm{GL}\left(n,F\right)×\mathrm{GL}\left(m,F\right)$ 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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