Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The controlling $L_\infty$-algebra, cohomology and homotopy of embedding
  tensors and Lie-Leibniz triples   In this paper, we first construct the controlling algebras of embedding
tensors and Lie-Leibniz triples, which turn out to be a graded Lie algebra and
an $L_\infty$-algebra respectively. Then we introduce representations and
cohomologies of embedding tensors and Lie-Leibniz triples, and show that there
is a long exact sequence connecting various cohomologies. As applications, we
classify infinitesimal deformations and central extensions using the second
cohomology groups. Finally, we introduce the notion of a homotopy embedding
tensor which will induce a Leibniz$_\infty$-algebra. We realize Kotov and
Strobl's construction of an $L_\infty$-algebra from an embedding tensor, to a
functor from the category of homotopy embedding tensors to that of
Leibniz$_\infty$-algebras, and a functor further to that of
$L_\infty$-algebras.

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The categories of this paper are: gr-qc
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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: physics
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The categories of this paper are: cs
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol