copula

A copula is a word or function that links the subject of a sentence to a subject complement, forming a predicative link. In linguistics, the term is used to describe copular constructions in which the predicate is not an action but a property, identity, or state. The most common example is the verb “to be” in many languages, with forms such as am, is, are, was, and were in English. The copula is central to statements about what something is or how it appears.

In English and many other languages, the copula can take various predicative complements, including adjectives, nouns, or prepositional phrases. For example: “The sky is blue” (predicative adjective), “She became a doctor” (predicative noun), and “The cake tastes delicious” (predicative adjective). Some verbs beyond be—such as become, seem, appear, and remain—are also considered copular or semi-copular, linking subject and predicate without expressing primary action.

Cross-linguistic variation is common. Some languages use an overt copula in all tenses, while others omit an explicit copula in the present tense or use different particles or word order to mark predication. In many languages with null copulas, the predicate exists without a distinct linking verb in certain tenses.

In statistics, a copula is a mathematical function that joins multivariate distributions to their univariate marginals, capturing the dependence structure between variables. Sklar’s theorem states that any joint distribution can be expressed in terms of its marginals and a copula. Common examples include the Gaussian copula and various Archimedean copulas, widely used in finance, engineering, and the natural sciences to model correlated outcomes.