Category of sheaves

In mathematics, particularly in topology and algebraic geometry, a "sheaf" is a way to systematically keep track of local data attached to open sets of a space. Imagine each open set as a neighborhood where you can gather information, like measuring temperature in different areas. A category of sheaves organizes these local measurements, ensuring that the information fits together nicely across overlapping areas. This approach allows mathematicians to work with complex structures by focusing on local properties and how they connect globally, facilitating deeper insights into spatial relationships and continuity.