# Completeness of the induced cotorsion pairs in functor categories

11 Feb 2021 Zhenxing Di Liping Li Li Liang Fei Xu

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... (read more)

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# Categories

• REPRESENTATION THEORY
• K-THEORY AND HOMOLOGY