Gluing Data categories and gluing data functors

Sophie Marques; Damas Mgani

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arXiv · 2304.14093

Gluing Data categories and gluing data functors

Sophie Marques·Damas Mgani

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Abstract

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.

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BibTeX RIS

Sophie Marques, Damas Mgani. 2023-04-27. Gluing Data categories and gluing data functors. https://arxiv.org/abs/2304.14093

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