Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the infinity category of homotopy Leibniz algebras   We discuss various concepts of $\infty$-homotopies, as well as the relations
between them (focussing on the Leibniz type). In particular
$\infty$-$n$-homotopies appear as the $n$-simplices of the nerve of a complete
Lie ${\infty}$-algebra. In the nilpotent case, this nerve is known to be a Kan
complex \cite{Get09}. We argue that there is a quasi-category of
$\infty$-algebras and show that for truncated $\infty$-algebras, i.e.
categorified algebras, this $\infty$-categorical structure projects to a strict
2-categorical one. The paper contains a shortcut to $(\infty,1)$-categories, as
well as a review of Getzler's proof of the Kan property. We make the latter
concrete by applying it to the 2-term $\infty$-algebra case, thus recovering
the concept of homotopy of \cite{BC04}, as well as the corresponding
composition rule \cite{SS07}. We also answer a question of \cite{BS07} about
composition of $\infty$-homotopies of $\infty$-algebras.

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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg