Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Higher commutator conditions for extensions in Mal'tsev categories   We define a Galois structure on the category of pairs of equivalence
relations in an exact Mal'tsev category, and characterize central and double
central extensions in terms of higher commutator conditions. These results
generalize both the ones related to the abelianization functor in exact
Mal'tsev categories, and the ones corresponding to the reflection from the
category of internal reflexive graphs to the subcategory of internal groupoids.
Some examples and applications are given in the categories of groups,
precrossed modules, precrossed modules of Lie algebras, and compact groups.

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The categories of this paper are: econ
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
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The categories of this paper are: cs
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The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
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The categories of this paper are: nlin
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn