Triangular Matrix Categories II: Recollements and functorially finite subcategories

10 Mar 2019 León-Galeana Alicia Ortiz-Morales Martín Vargas Valente Santiago

In this paper we continue the study of triangular matrix categories $\mathbf{\Lambda}=\left[ \begin{smallmatrix} \mathcal{T} & 0 \\ M & \mathcal{U} \end{smallmatrix}\right]$ initiated in [21]. First, given an additive category $\mathcal{C}$ and an ideal $\mathcal{I}_{\mathcal{B}}$ in $\mathcal{C}$, we prove a well known result that there is a canonical recollement $\xymatrix{\mathrm{Mod}(\mathcal{C}/\mathcal{I}_{\mathcal{B}})\ar[r]_{} & \mathrm{Mod}(\mathcal{C})\ar[r]_{}\ar@<-1ex>[l]_{}\ar@<1ex>[l]_{} & \mathrm{Mod}(\mathcal{B})\ar@<-1ex>[l]_{}\ar@<1ex>[l]_{}}$... (read more)

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