Gluing Data categories and gluing data functors
Category Theory
2024-03-04 v3 Algebraic Geometry
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.
Cite
@article{arxiv.2304.14093,
title = {Gluing Data categories and gluing data functors},
author = {Sophie Marques and Damas Mgani},
journal= {arXiv preprint arXiv:2304.14093},
year = {2024}
}