2023/04/27 by Sophie Marques, Marques, Sophie, Damas Mgani +1
Computer Science · Earth and Planetary Sciences · #14A15 #18F20 #18F60 #Advanced Computational Techniques and Applications #Algebraic Geometry (math.AG) #Category Theory (math.CT) #Distributed and Parallel Computing Systems #FOS: Mathematics #Geological Modeling and Analysis
paper · pdf · doi:10.48550/arxiv.2304.14093
openalex publication_date 2023/04/27 · openalex created_date 2023/04/30 · openalex updated_date 2026/07/28
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.