Groupoids

A groupoid is a mathematical structure similar to a group, but more flexible. While groups consist of elements that can be combined consistently (like adding numbers), groupoids allow for elements that can only be combined if they are related in a specific way, typically having a "source" and "target." Think of it as a network of transformations or connections between different objects where composition is only possible when the end of one matches the start of another. This makes groupoids useful for describing systems with localized symmetries or partial symmetries, such as shapes, symmetries in geometry, or network transformations.