Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the regular representation of an (essentially) finite 2-group   The regular representation of an essentially finite 2-group $\mathbb{G}$ in
the 2-category $\mathbf{2Vect}_k$ of (Kapranov and Voevodsky) 2-vector spaces
is defined and cohomology invariants classifying it computed. It is next shown
that all hom-categories in $\mathbf{Rep}_{\mathbf{2Vect}_k}(\mathbb{G})$ are
2-vector spaces under quite standard assumptions on the field $k$, and a
formula giving the corresponding "intertwining numbers" is obtained which
proves they are symmetric. Finally, it is shown that the forgetful 2-functor
${\boldmath$\omega$}:\mathbf{Rep}_{\mathbf{2Vect}_k}(\mathbb{G})\To\mathbf{2Vect}_k$
is representable with the regular representation as representing object. As a
consequence we obtain a $k$-linear equivalence between the 2-vector space
$\mathbf{Vect}_k^{\mathcal{G}}$ of functors from the underlying groupoid of
$\mathbb{G}$ to $\mathbf{Vect}_k$, on the one hand, and the $k$-linear category
$\mathcal{E} nd({\boldmath$\omega$})$ of pseudonatural endomorphisms of
${\boldmath$\omega$}$, on the other hand. We conclude that $\mathcal{E}
nd({\boldmath$\omega$})$ is a 2-vector space, and we (partially) describe a
basis of it.

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The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
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The categories of this paper are: physics
0
The categories of this paper are: hep-ph