category

A category is a collection of things that share a common feature or purpose, allowing them to be treated as a group. In everyday use, people create categories to organize objects, ideas, or activities, such as fiction and non-fiction books, foods, or genres. The act of forming such groups is called categorization. The term comes from Greek katēgoria, meaning a general form of classification.

In information science and libraries, categories underpin classification systems, catalogs, and search tools. Taxonomies or ontologies arrange items into hierarchies or facets to support discovery. Examples include library classification schemes, product taxonomies in e-commerce, and topic tags on websites. Proper categorization improves retrieval, comparison, and analysis by providing shared references.

In mathematics, a category is a formal structure studied in category theory. A category consists of objects and arrows (morphisms) between objects, with rules for composing arrows and for identity morphisms. This abstraction generalizes many mathematical constructions. Examples include the category of sets, whose objects are sets and whose arrows are functions, and the category of groups. Categories may be small or large, and duality reveals symmetrical aspects.

In statistics and data analysis, a category refers to a qualitative value assigned to observations, such as gender, color, or response options. Categories may be nominal (no intrinsic order) or ordinal (ordered). Coding, labeling, and cross-tabulation rely on categorization to summarize, compare, and interpret data.