Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Left-invariant vector fields on a Lie 2-group   A Lie 2-group $G$ is a category internal to the category of Lie groups.
Consequently it is a monoidal category and a Lie groupoid. The Lie groupoid
structure on $G$ gives rise to the Lie 2-algebra $\mathbb{X}(G)$ of
multiplicative vector fields, see (Berwick-Evans -- Lerman). The monoidal
structure on $G$ gives rise to a left action of the 2-group $G$ on the Lie
groupoid $G$, hence to an action of $G$ on the Lie 2-algebra $\mathbb{X}(G)$.
As a result we get the Lie 2-algebra $\mathbb{X}(G)^G$ of left-invariant
multiplicative vector fields. On the other hand there is a well-known
construction that associates a Lie 2-algebra $\mathfrak{g}$ to a Lie 2-group
$G$: apply the functor $\mathsf{Lie}: \mathsf{Lie Groups} \to \mathsf{Lie
Algebras}$ to the structure maps of the category $G$. We show that the Lie
2-algebra $\mathfrak{g}$ is isomorphic to the Lie 2-algebra $\mathbb{X}(G)^G$
of left invariant multiplicative vector fields.

31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics