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arXiv · 2605.23060

Reflections and Sheafifications in Algebraic and Topological Categories

Julio César Hernández Arzusa·Hernán Giraldo·Samir Rivero Castro
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Abstract

In this article, we develop an explicit categorical realization of sheafification based on colimits, products, and subobjects, emphasizing its behavior in algebraic and topological-algebraic settings. We prove that if $\mathcal{C}$ is a reflective subcategory of a category $\mathcal{A}$, then the presheaf category $\mathbf{Psh}(X,\mathcal{C})$ is reflective in $\mathbf{Psh}(X,\mathcal{A})$. We further investigate the interaction between reflections and sheafification, obtaining natural conditions under which these constructions are naturally isomorphic.

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Julio César Hernández Arzusa, Hernán Giraldo, Samir Rivero Castro. 2026-05-21. Reflections and Sheafifications in Algebraic and Topological Categories. https://arxiv.org/abs/2605.23060

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