Signature (universal algebra)

In mathematics, a signature for an algebraic structure A, as used in universal algebra, model theory, categorical logic and type theory, is a list of all the operations available in A. It is understood that these each have an arity n ≥ 0. To allow for external operations it is assumed that there may be various 'kinds', so that each operation also has a type, namely the cartesian products of kinds that are accepted and returned by the operation.