Sheaves

Sheaves are mathematical tools that systematically organize local data across a space, ensuring it can be consistently combined into a global picture. Imagine covering a landscape with overlapping maps; each map has specific details, and where they overlap, the information must agree. Sheaves formalize this idea, allowing us to track local information (like functions or measurements) and understand how these local pieces fit together seamlessly across the entire space. They are fundamental in fields like topology and algebraic geometry, enabling rigorous analysis of complex structures by piecing together simpler parts.