Geodesic
Triangular matrix categories over quasi-hereditary categories
Glasgow mathematical journal, Tome 66 (2024) no. 3, pp. 449-470

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DOI

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.
DOI : 10.1017/S0017089524000053
Mots-clés : Functor Categories, Matrix Categories, Path Categories, Quasihereditary Categories 
Cruz, Rafael Francisco Ochoa De La; Morales, Martin Ortíz; Vargas, Valente Santiago. Triangular matrix categories over quasi-hereditary categories. Glasgow mathematical journal, Tome 66 (2024) no. 3, pp. 449-470. doi: 10.1017/S0017089524000053
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     title = {Triangular matrix categories over quasi-hereditary categories},
     journal = {Glasgow mathematical journal},
     pages = {449--470},
     year = {2024},
     volume = {66},
     number = {3},
     doi = {10.1017/S0017089524000053},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089524000053/}
}
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