Construction of ideal cotorsion pairs via recollements of triangulated categories
Colloquium Mathematicum
MSC: Primary 18G15; Secondary 18G80, 16E30
DOI: 10.4064/cm9723-4-2026
Published online: 6 October 2026
Abstract
Let $(\mathcal {T}’,\mathcal {T},\mathcal {T}”)$ be a recollement of triangulated categories. A complete ideal cotorsion pair in $\mathcal {T}$ induces complete ideal cotorsion pairs in $\mathcal {T}’$ and $\mathcal {T}”$. In addition, if $(\mathcal {I}, \mathcal {I}^\perp )$ and $(\mathcal {J},\mathcal {J}^\perp )$ are two complete ideal cotorsion pairs in a triangulated category, then $(\mathcal {I}\cap \mathcal {J}, \langle \mathcal {I}^\perp ,\mathcal {J}^\perp \rangle )$ is also a complete ideal cotorsion pair. By this method, starting from two complete ideal cotorsion pairs in $\mathcal {T}’$ and $\mathcal {T}”$, one can induce a family of complete ideal cotorsion pairs in $\mathcal {T}$.
