Reflections and Sheafifications in Algebraic and Topological Categories
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866916037991071744 |
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| author | Arzusa, Julio César Hernández Giraldo, Hernán Castro, Samir Rivero |
| author_facet | Arzusa, Julio César Hernández Giraldo, Hernán Castro, Samir Rivero |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_23060 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Reflections and Sheafifications in Algebraic and Topological Categories Arzusa, Julio César Hernández Giraldo, Hernán Castro, Samir Rivero General Topology 18F20, 18A40, 22A05, 54B40 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. |
| title | Reflections and Sheafifications in Algebraic and Topological Categories |
| topic | General Topology 18F20, 18A40, 22A05, 54B40 |
| url | https://arxiv.org/abs/2605.23060 |