Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Completeness of the induced cotorsion pairs in functor categories   This paper focuses on a question raised by Holm and J{\o}rgensen, who asked
if the induced cotorsion pairs $(\Phi({\sf X}),\Phi({\sf X})^{\perp})$ and
$(^{\perp}\Psi({\sf Y}),\Psi({\sf Y}))$ in $\mathrm{Rep}(Q,{\sf{A}})$ -- the
category of all $\sf{A}$-valued representations of a quiver $Q$ -- are complete
whenever $(\sf X,\sf Y)$ is a complete cotorsion pair in an abelian category
$\sf{A}$ satisfying some mild conditions. Recently, Odaba\c{s}{\i} gave an
affirmative answer if the quiver $Q$ is rooted and the cotorsion pair $(\sf
X,\sf Y)$ is further hereditary. In this paper, we improve Odaba\c{s}{\i}'s
work by removing the hereditary assumption on the cotorsion pair. As an
application, we show under certain mild conditions that if a subcategory $\sf
L$, which is not necessarily closed under direct summands, of $\sf A$ is
special precovering (resp., preenveloping), then $\Phi(\sf L)$ (resp.,
$\Psi(\sf L)$) is special precovering (resp., preenveloping) in
$\mathrm{Rep}(Q,{\sf{A}})$.

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The categories of this paper are: q-bio
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The categories of this paper are: nlin
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The categories of this paper are: comp-gas
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The categories of this paper are: physics
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The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
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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: q-alg