Let $\mathcal{ B}$ be an abelian category with enough projective objects and enough injective objects and let $\mathcal{ A}=\mathcal{ B}\ltimes_\eta\mathsf{ F}$ be an $\eta$-extension of $\mathcal{ B}$. Given a cotorsion pair $(\mathcal{ X},\;\mathcal{ Y})$ in $\mathcal{ B}$, we construct a cotorsion pair $(^{ \perp}{ \mathsf{ U}^{ -1}(\mathcal{ Y})}, \mathsf{ U}^{ -1}(\mathcal{ Y}))$ in $\mathcal{ A}$ and a cotorsion pair $(\Delta(\mathcal{ X}),\;\Delta(\mathcal{ X})^\perp)$ in $\mathcal{ A}$ for $\mathsf{ F}^2=0$. In addition, the heredity and completeness of these cotorsion pairs are studied. Finally, we give some applications and examples in comma categories, some Morita context rings and trivial extensions of rings.
Categories: math.RT