Definition of "codomain" [codomain]

• The target space into which a function maps elements of its domain. It always contains the range of the function, but can be larger than the range if the function is not surjective. (noun)

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• "For example, if a unary function is considered as a set of ordered pairs, then the domain and codomain are given by the first and second projections, respectively."
• "Combinatory terms are thought of as functions, and functions are thought to have a domain (a set of possible inputs) and a codomain (a set of possible outputs)."
• "Category theory, where functions are components of categories (without a set theoretic reduction assumed), retains the notions of a domain and a codomain; moreover, every function has a unique domain and codomain."