Enriched Categories

Enriched categories are a concept in category theory, a branch of mathematics. At their core, they extend the basic idea of categories by adding extra structure to the relationships (morphisms) between objects. Instead of just considering morphisms as arrows connecting objects, enriched categories allow these relationships to carry more information. For example, in a "metric enriched category," the morphisms can represent distances between objects, providing a way to discuss not only whether one object relates to another but also how closely or distantly they are connected. This framework helps mathematicians model complex systems more effectively.