Sheaf

Summary

A sheaf on a topological space assigns to each open set a set of data, such as functions, with restriction maps to smaller open sets. The data must be determined by their local pieces, and compatible local pieces must glue together. Sheaves organise local information on a space and measure how it fails to be global. They are the language of modern algebraic geometry, where a scheme is a space with a sheaf of rings. They are also the coefficients of sheaf cohomology in topology and complex analysis.