Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $3$-$Lie_\infty$-algebras and $3$-Lie 2-algebras   In this paper, we introduce the notions of a $3$-$Lie_\infty$-algebra and a
3-Lie 2-algebra. The former is a model for a 3-Lie algebra that satisfy the
fundamental identity up to all higher homotopies, and the latter is the
categorification of a 3-Lie algebra. We prove that the 2-category of 2-term
$3$-$Lie_\infty$-algebras is equivalent to the 2-category of 3-Lie 2-algebras.
Skeletal and strict 3-Lie 2-algebras are studied in detail. A construction of a
3-Lie 2-algebra from a symplectic 3-Lie algebra is given.

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The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
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The categories of this paper are: eess