Intuitive

Locality is a fundamental concept in modern physics and means that object can only be influenced by their immediate surroundings, i.e. locally.

For example, a billiard ball only starts rolling when it gets hit with something. It doesn't start rolling around magically.

This concept is made even more precise through special relativity. The fundamental fact at the heart of special relativity is that nothing can move with a velocity faster than the speed of light. This means tells us immediately how far an object can be away to influence another one since the effect always needs time to travel to the object in question.

Concrete

Abstract

Q:Locality principle - What does it mean physically?

A: Global field configurations have to be obtained by summing up local data. That means by gluing local field configurations together.

Q: What does it mean mathematically?

A: This is captured by the theory of sheaves.

https://ncatlab.org/schreiber/files/EggertsonGaugeAndGroupoids14.pdf

Why is it interesting?