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arXiv · 2509.18290

Functor categories, Recollements, Triangular Matrix category

M. L. S. Sandoval-Miranda·V. Santiago-Vargas·E. O. Velasco-Páez
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Abstract

In this paper we study triangular matrix categories using the theory of recollements of abelian categories. Given a triangular matrix category we construct two canonical recollements. We show that if certain funtors of these recollements are exact then the category appearing in the middle term is actually a triangular matrix category. This result is a generalization of one given by Liping Li in \cite{LipingLi}. We also show that if $\mathrm{Mod}(\mathcal{C})$ admits a nontrivial torsion pair by abelian categories then $\mathcal{C}$ is equivalent to a triangular matrix category.

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BibTeXRIS

M. L. S. Sandoval-Miranda, V. Santiago-Vargas, E. O. Velasco-Páez. 2025-09-22. Functor categories, Recollements, Triangular Matrix category. https://arxiv.org/abs/2509.18290

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