Catégories

Catégories refers to the idea of organizing items, ideas, or phenomena into classes that share common properties. In everyday usage, categorization supports reasoning and communication by structuring knowledge, from biological taxonomy and library catalogs to product classification and metadata schemas. Categories can be hierarchical, linked, or networked, depending on the purpose and context.

In mathematics, category theory provides a formal framework for studying structures and the relationships between them. A category consists of objects and arrows (morphisms) between objects, with rules for composing arrows and for identity arrows. These rules (associativity and identity) enable abstract analysis of structures across different areas by focusing on relationships rather than internal content. Core concepts include functors, which map between categories, and natural transformations, which relate functors. Universal properties describe objects determined uniquely by their relationships. Common examples are the categories of sets, groups, and topological spaces. Category theory has become a foundational language in mathematics and has influenced computer science, logic, and physics.

In information science and library science, categorization underpins taxonomies, ontologies, and metadata schemas. These systems organize documents, data, and digital resources to improve discovery, interoperability, and reasoning across platforms and domains.

Historically, the term étendue of the concept spans many fields, but the formal mathematical use emerged in the 1940s with Eilenberg and Mac Lane. In French contexts, théorie des catégories is the field, and caté gories can denote either multiple categories or broad classifications within a domain.