Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $n$-abelian and $n$-exact categories   We introduce $n$-abelian and $n$-exact categories, these are analogs of
abelian and exact categories from the point of view of higher homological
algebra. We show that $n$-cluster-tilting subcategories of abelian (resp.
exact) categories are $n$-abelian (resp. $n$-exact). These results allow to
construct several examples of $n$-abelian and $n$-exact categories. Conversely,
we prove that $n$-abelian categories satisfying certain mild assumptions can be
realized as $n$-cluster-tilting subcategories of abelian categories. In analogy
with a classical result of Happel, we show that the stable category of a
Frobenius $n$-exact category has a natural $(n+2)$-angulated structure in the
sense of Gei\ss-Keller-Oppermann. We give several examples of $n$-abelian and
$n$-exact categories which have appeared in representation theory, commutative
ring theory, commutative and non-commutative algebraic geometry.

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The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin