Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A sufficient criterion for homotopy cartesianess   Suppose given a commutative quadrangle in a Verdier triangulated category
such that there exists an induced isomorphism on the horizontally taken cones.
Suppose that the endomorphism ring of the initial or the terminal corner object
of this quadrangle satisfies a finiteness condition. Then this quadrangle is
homotopy cartesian.

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The categories of this paper are: chem-ph
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The categories of this paper are: cs
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
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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: hep-ex
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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The categories of this paper are: eess