Sheaf theory

Sheaf theory is a mathematical framework that systematically organizes local information on a space and explains how these local pieces relate to form a complete global picture. Think of it as a rulebook assigning data to small regions—like measurements in different parts of a landscape—and providing conditions to consistently piece these local data together into a unified understanding of the entire space. It’s used in areas like topology, geometry, and physics to analyze how local properties influence global structures, ensuring that local observations fit together smoothly to reveal the overall structure.