arXiv subjects

V. Santiago-Vargas

Publications and source records attributed to V. Santiago-Vargas.

2 recordsLinked to original sources

arXiv2026

Homological Epimorphisms and Hochschild-Mitchell Cohomology

In this work, we study the Hochschild-Mitchell Cohomology of triangular matrix categories. Given a triangular matrix category $Λ=\left[ \begin{smallmatrix} \mathcal{T} & 0 \\ M & \mathcal{U} \end{smallmatrix}\right]$, we investigate the relationship of the Hochschild-Mitchell cohomologies $H^{i}(Λ)$ and $H^{i}(\mathcal{U})$ of $Λ$ and $\mathcal{U}$ respectively; and we show that they can be connected by a long exact sequence. This result extend the well-known result of Michelana-Platzeck given in [S. Michelena, M. I. Platzeck. {\it{Hochschild cohomology of triangular matrix algebras}}. J. Algebra 233, (2000) 502-525].

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arXiv2025

Functor categories, Recollements, Triangular Matrix category

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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