Gluing Data categories and gluing data functors
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909124209410048 |
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| author | Marques, Sophie Mgani, Damas |
| author_facet | Marques, Sophie Mgani, Damas |
| contents | We present a novel approach to the concept of gluing in mathematics by introducing the notions of a gluing data category and a gluing data functor. Our work provides a formal categorical characterization of the notion of gluing in algebraic geometry. By using this characterization, we are able to describe gluing in a unified way that applies to a wide range of mathematical structures, including topological spaces, presheaves, sheaves, ringed topological spaces, locally ringed topological spaces, and schemes. Our results provide a fresh perspective on gluing that is both abstract and formal, offering a deeper understanding of this fundamental concept in mathematics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_14093 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Gluing Data categories and gluing data functors Marques, Sophie Mgani, Damas Category Theory Algebraic Geometry 14A15, 18F20, 18F60, We present a novel approach to the concept of gluing in mathematics by introducing the notions of a gluing data category and a gluing data functor. Our work provides a formal categorical characterization of the notion of gluing in algebraic geometry. By using this characterization, we are able to describe gluing in a unified way that applies to a wide range of mathematical structures, including topological spaces, presheaves, sheaves, ringed topological spaces, locally ringed topological spaces, and schemes. Our results provide a fresh perspective on gluing that is both abstract and formal, offering a deeper understanding of this fundamental concept in mathematics. |
| title | Gluing Data categories and gluing data functors |
| topic | Category Theory Algebraic Geometry 14A15, 18F20, 18F60, |
| url | https://arxiv.org/abs/2304.14093 |