Functoriality

Functoriality is a concept from mathematics that describes a consistent way of translating structures from one context to another. Think of it like a function that maps objects and their relationships (like shapes and how they connect) in one setting to another, while preserving the connections. This means if two objects are related in the first setting, their images remain related in the second. Functoriality ensures that these mappings respect the structure's rules, maintaining the integrity of relationships across different systems, facilitating meaningful comparisons and transformations within mathematical frameworks.