Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on abelian quotient categories   Let C be a triangulated category with a Serre functor S and X a non-zero
contravariantly finite rigid subcategory of C. Then X is cluster tilting if and
only if the quotient category C/X is abelian and S(X)=X[2]. As an application,
this result generalizes work by Beligiannis.

10
The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg