Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pushouts of categories, derived limits and colimits   In a paper by Ford, it is claimed that to any pushout square of categories
with all involved functors injective, there is associated an exact
"Mayer--Vietoris" sequence of derived (co)limits. We provide a counter-example
to this general statement. Further, we construct the Mayer--Vietoris sequence
under some restrictions that cover the well-known case of a pushout square of
group monomorphisms.

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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: cs
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas