Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Addendum to 'Direct limits in the heart of a t-structure: The case of a
  torsion pair'   Let $\mathcal{G}$ be a Grothendieck category, let
$\mathbf{t}=(\mathcal{T},\mathcal{F})$ be a torsion pair in $\mathcal{G}$ and
let $(\mathcal{U}_\mathbf{t},\mathcal{W}_\mathbf{t})$ be the associated
Happel-Reiten-Smal$\o$ t-structure in the derived category
$\mathcal{D}(\mathcal{G})$. We prove that the heart of this t-structure is a
Grothendieck category if, and only if, the torsionfree class $\mathcal{F}$ is
closed under taking direct limits in $\mathcal{G}$.

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The categories of this paper are: chem-ph
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The categories of this paper are: econ
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
3
The categories of this paper are: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: math-ph
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The categories of this paper are: nlin