Triangular matrix categories over quasi-hereditary categories

In this paper, we prove that the lower triangular matrix category $\Lambda =\left [ \begin{smallmatrix} \mathcal{T}&0\\ M&\mathcal{U} \end{smallmatrix} \right ]$ , where $\mathcal{T}$ and $\mathcal{U}$ are $\textrm{Hom}$ -finite, Krull–Schmidt $K$ -quasi-hereditary categories and $M$ is an $...

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Bibliographic Details
Published in:Glasgow mathematical journal 2024-09, Vol.66 (3), p.449-470
Main Authors: Ochoa De La Cruz, Rafael Francisco, Ortíz Morales, Martin, Santiago Vargas, Valente
Format: Article
Language:English
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Modules
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Summary:In this paper, we prove that the lower triangular matrix category $\Lambda =\left [ \begin{smallmatrix} \mathcal{T}&0\\ M&\mathcal{U} \end{smallmatrix} \right ]$ , where $\mathcal{T}$ and $\mathcal{U}$ are $\textrm{Hom}$ -finite, Krull–Schmidt $K$ -quasi-hereditary categories and $M$ is an $\mathcal{U}\otimes _K \mathcal{T}^{op}$ -module that satisfies suitable conditions, is quasi-hereditary. This result generalizes the work of B. Zhu in his study on triangular matrix algebras over quasi-hereditary algebras. Moreover, we obtain a characterization of the category of the $_\Lambda \Delta$ -filtered $\Lambda$ -modules.
ISSN:0017-0895
1469-509X
DOI:10.1017/S0017089524000053